Long Test 2 – Feb. 13 (Monday) -finding the restrictions/excluded values -solving rational equations - translating phrases - word problems

MOTION PROBLEMS

Thinking time What is the average speed of a car which traveled 30km in 20 minutes? (kph) What is the average speed of a car which traveled 30km in 20 minutes? (kph) How far will a jogger reach in 2 hours if he jogs at an average pace of 20mph? How far will a jogger reach in 2 hours if he jogs at an average pace of 20mph? How long will a 75 mile trip take at an average speed of 20 mph? How long will a 75 mile trip take at an average speed of 20 mph?

Rate x Time = Distance Rate x Time = Distance Distance = Time Distance = Time Rate Rate Distance = Rate Distance = Rate Time Time D RT

Motion in Opposite Directions Two cars leave from the same place at the same time and travel in opposite directions. One car travels at 55 mph and the other at 75 mph. After how many hours will they be 520 miles apart? miles

Two cars leave from the same place at the same time and travel in opposite directions. One car travels at 55 mph and the other at 75 mph. After how many hours will they be 520 miles apart? RateTimeDistance Car 155T55t Car 275t75t

1) Two buses leave the same station at the same time and travel in opposite directions. After 8 hrs they are 360 km apart. The speed of the faster bus is 3 kph less than twice the speed of the slower bus. Find the rate of each bus.

There are two trains. The Rabbit heads north on the expressway at 45kph. Exactly 12 min after, the Panther follows at a steady speed of 54kph. How long does it take the Panther to overtake the Rabbit? Motion in the same Direction 12 minutes after

There are two trains. The Rabbit heads north on the expressway at 45kph. Exactly 12 min after, the Panther follows at a steady speed of 54kph. How long does it take the Panther to overtake the Rabbit? The Panther travels for 12 minutes less than (12 mins = 1/5 hr) the Rabbit because it travels 12 minutes later. RateTimeDistance Rabbit45x (x + 1 ) 5 Panther54x54x When the Panther overtakes the Rabbit, the distances will be equal.

2) Mimi left home on her bicycle at an average rate of 6 kph. One hour later, her brother Mon set out to overtake her at an average rate of 8 kph. In how many hours will Mon overtake Mimi?

While waiting for a train, Alvin takes a bus ride at 60 kph to a certain point and then walks back leisurely at 10 kph. The bus ride takes 15 minutes less than his walking. How far does he walk and for how long? Round-trip 15 minutes = ¼ hr

While waiting for a train, Alvin takes a bus ride at 60 kph to a certain point and then walks back leisurely at 10 kph. The bus ride takes 15 minutes less than his walking. How far does he walk and for how long? In a round-trip, the 2 distances are equal. RateTimeDistance Walk10x10x Ride60x – (x – 1) 4

A pilot flew from one city to another city averaging 150 mph. Later, it flew back to the first city averaging 100 mph. The total flying time was 5 hours. How far apart are the cities?

NSM 2 Chap. 4 Ex. 16 (p. 135 ) A motorist took 3 1/3 hour to drive 160 km. He drove part of the way at an average speed of 50kph and the rest of the way at 45kph. What is the distance traveled at 50kph? RateTimeDistance 1 st part50x 50 x 2 nd part45160-x x The total time taken was 3 1 hours. 3

NSM 2 Chap. 4 Ex. 17 (p. 136 ) Mr. Tan makes monthly visits to his parents in Malacca, a distance of 240 km from Singapore. He finds that if he increases the average speed by 10 kph, he could save a total of 20 minutes for the journey. Find the original speed of Mr. Tan.

PROBLEM 2 The Po family traveled 135 miles by train and the traveled 855 miles by plane. The speed of the plane was three times the speed of the train. If the total time of the trip was 6 hours, what was the speed of the train?

PROBLEM 3 Andrea can drive 100 miles to work in the same time that it takes her to drive 60 mph to a friends house. When driving to her friend’s house, Andrea drives 20 mph slower than when she drives to work. How fast does she drive going to work?

HOMEWORK Answer Exercise 4h NSM Book 2 Page 137 numbers 12, 13, 14, and 17 Show complete solutions (1 whole pad paper)

12) A man walked for some distance at 8 kph and for an equal distance at 5 kph. The total time he took was 3 ¼ hours. Find the total distance he walked. RateTimeDistance 1 st half 8d8d8 d 2 nd half 5d5d5 d Total time was 3 ¼ or 13 hours. 4

Solution He walked 10 km halfway, so the total distance he walked is 20 km.

Total time was 7 ¾ or 31 hours ) A man cycled for some time at 16 kph and returned at 15 kph. The total time taken was 7 ¾ hours. Find the total distance he cycled. RateTimeDistance Going to 16d 16 d Going back 15d 15 d

Solution

Distance traveled going to and going back are equal. A cyclist goes from one village to another at 28 kph. He returns at 24 kph. If the return journey takes two hours longer than the outward journey, what is the distance between the villages? RateTimeDistance Going to 28x28x Going back 24x + 224(x + 2)

Solution Distance between the villages = 28(12) = 336 km

Mr. Ong makes regular business trips to Kuala Lumpur, a distance of 420 km from Singapore. a)On his way to KL he travels along the trunk road at an average speed of x kph. Write down an expression, in terms of x, for the time taken, in hours, to travel from Singapore to KL.

b) On his return journey to SG, he travels along the NS Highway and increases the average speed by 15 kph. Write down an expression, in terms of x, for the time taken, in hours, to travel from KL to SG.

c)If the time difference between the two journeys is 40 minutes, form an equation in x and show that it reduces to x x – 9450 = 0. d) Solve the equation and find the time taken for the trip from SG to KL.