Question

12. A train leaves the city at 2 pm. A second train leaves the city at 4 pm and follows the first train. The second train's speed is 32 km/h faster than the first train's speed. If the second train
overtakes the first train at 8 pm, find the speeds of both the trains.​

Answer 1

Step-by-step explanation:

Let

Letv = the speed of the first train

Letv = the speed of the first trainv + 162 = the speed of the second train

Letv = the speed of the first trainv + 162 = the speed of the second traint1 = 10 - 2 = 8 hr the time of the first time

Letv = the speed of the first trainv + 162 = the speed of the second traint1 = 10 - 2 = 8 hr the time of the first timet2 = 10 - 8 = 2 ht the time of the second time

Letv = the speed of the first trainv + 162 = the speed of the second traint1 = 10 - 2 = 8 hr the time of the first timet2 = 10 - 8 = 2 ht the time of the second timeSince both trains travel the same distance we have:

Letv = the speed of the first trainv + 162 = the speed of the second traint1 = 10 - 2 = 8 hr the time of the first timet2 = 10 - 8 = 2 ht the time of the second timeSince both trains travel the same distance we have:vt1 = (v + 162)t2 (we use the formula distance = speed*time)

Letv = the speed of the first trainv + 162 = the speed of the second traint1 = 10 - 2 = 8 hr the time of the first timet2 = 10 - 8 = 2 ht the time of the second timeSince both trains travel the same distance we have:vt1 = (v + 162)t2 (we use the formula distance = speed*time)8v = 2(v + 162)

v = 54 mph

v = 54 mphv + 162 = 54 + 162 = 216 mph

v = 54 mphv + 162 = 54 + 162 = 216 mphThe speed of the first train is 54 mph while the speed of the second train is 216 mph.

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