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Submitted by: Karin

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Dear Jay, You must use the distance formula to solve this problem. We will use the distance formula for the freight train and the passenger train. freight: d= rt passenger: d = rt We know that the passenger train takes 2 less hours than the freight train. We don't know how long the freight train takes, so we are going to let our variable x = the number of hours for the freight train. So we know: freight: time = x, rate = 64km/hour passenger: time = x -2 rate = 96 km/hour We also know that the two trains are traveling the same distance, so we are going to set these two equations equal to each other. freight distance = passenger distance rt = rt 64x = 96(x-2) 64x = 96x - 192 Distribute 64x - 96x = 96x -96x -192 Subtract 96x from both sides. -32x = -192 -32x/-32 = -192/-32 x = 6 Since x = 6 we know that the freight train takes 6 hours and the passenger train takes 4 hours. So, let's figure out the distance - it should be the same for both trains. freight: d= rt d = 64(6) d = 384 km passenger: d = rt d = 96(4) d = 384 km Therefore, the distance is 384 km. Hope this helps! All the best, Karin

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