3.4 Rates 1. Solve problems involving two objects traveling in opposite directions. 2. Solve problems involving two objects traveling in the same direction.

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Presentation transcript:

3.4 Rates 1. Solve problems involving two objects traveling in opposite directions. 2. Solve problems involving two objects traveling in the same direction.

distance = rate ∙ time Rate Problems distance = distance d = d same direction distance 1 + distance 2 = total distance d1 + d2 = dt opposite directions Find rate and time for each vehicle.

Rate Problems d = d d1 + d2 = dt The trains will meet in 6.5 hours. What did we find? Did we answer the question? Two trains are traveling on parallel tracks toward each other from a distance of 533 miles. If the freight train is traveling at 27 miles per hour and the passenger train is moving at 55 miles per hour, how long will it take for them to meet each other? d = d d1 + d2 = dt 55t + 27t = 533 82t = 533 55 mph 27 mph t = 6.5 533 miles The trains will meet in 6.5 hours. d = r t Categories Rate Time Distance Passenger Freight 55 mph t = 6.5 55t 27 mph t 27t

Rate Problems d = d d1 + d2 = dt What did we find? Did we answer the question? Two planes leave Denver at the same time, one flying north and the other flying south. If the plane flying south is traveling at 653 miles per hour and the plane flying north is traveling 560 miles per hour, after how many hours will the planes be 2426 miles apart. d = d d1 + d2 = dt 653t + 560t = 2426 1213t = 2426 560 mph 653 mph t = 2 2426 miles The planes will be 2426 miles apart in 2 hours. d = r t Categories Rate Time Distance South North 653 mph t = 2 653t 560 mph t 560t

Morrison leaves Cincinnati at 4:00 pm, heading for NYC Morrison leaves Cincinnati at 4:00 pm, heading for NYC. Barbara leaves at 4:30 pm on the same highway, heading toward NYC. By driving 10 mph faster, Barbara overtakes Morrison at 7:30 pm. How fast is Barbara driving and how far have they traveled when Barbara catches up with Morrison? M B 4:00 d = d d1 + d2 = dt 3.5r = 3(r + 10) 4:30 + 10 mph 3.5r = 3r + 30 Be sure you answer the question that is asked!! 35r = 30r + 300 What did we find? 5r = 300 Did we answer the question? r = 60 How fast is Barbara driving? r + 10 = 60 + 10 = 70 mph How far have they traveled? d = rt = (70)(3) = 210 miles d = r t Categories Rate Time Distance Morrison Barbara r = 60 3.5 3.5 r r + 10 = 70 3 3(r + 10)

Rate Problems d = d d1 + d2 = dt What did we find? Did we answer the question? Monica and Chandler pass each other along a straight road traveling in opposite directions. Monica is driving at 40 mph and Chandler at 50 mph. In how many hours will the cars be 225 miles apart? Monica Chandler d = d d1 + d2 = dt 40 mph 50 mph 40t + 50t = 225 90t = 225 225 miles t = 2.5 They will be 225 miles apart in 2.5 hours. d = r t Categories Rate Time Distance Monica Chandler 40 mph t = 2.5 40t 50 mph t 50t

At 6 a. m. a freight train leaves Washington D. C. traveling at 50 mph At 6 a.m. a freight train leaves Washington D.C. traveling at 50 mph. At 9 a.m. a passenger train leaves the same station traveling in the same direction at 75 mph. How long will it take the passenger train to overtake the freight train? How far from the station will they be at that time? 6:00 50 mph d = d d1 + d2 = dt Freight train 50t = 75(t – 3) 9:00 75 mph 50t = 75t – 225 Passenger train – 25t = – 225 What did we find? t = 9 Did we answer the question? How long will it take for the passenger train to overtake the freight train? 6 hours How far from the station will they be at that time? d = rt = (50)(9) = 450 miles d = r t Categories Rate Time Distance Freight Passenger 50 t = 9 50t 75 t – 3 = 6 75(t – 3)