Question

At 10 a.m., a train leaves Salt Lake City traveling north at 40 miles per hour. At 2 p.m., another train leaves Salt Lake City traveling south at 50 miles per hour.
What time are the two trains the same distance from Salt Lake City?

Answer 1

The time the two trains are at the same distance from salt lake city is 6:am

What is rate?

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

Let the distance between salt lake city and the two trains be x and the time they are at the same distance x be t.

distance traveled by first train,

speed = distance/time

40 = x/t

making x subject of the equation and cross multiplying,

x = 40t--------------1

Also train 2 moved 4 hours later by 2pm, so the its time is t - 4

speed = distance /time

50 = x/t - 4

x = 50(t - 4)---------------2

Equating equations 1 and 2, we have

50(t - 4) = 40t

50t - 200 = 40t

50t - 40t = 200

10t = 200

t = 200/10

t = 20 hours

so the time the two trains will be at the same distance should be 20 hours from 10 am which is 6am the following day.

In conclusion the two trains will be at the same distance at 6am the following day.

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