Question

Train X is traveling at a constant speed of 30 miles per hour and Train Y is traveling at a constant speed of 40 miles per hour. If the two trains are traveling in the same direction along the same route but Train X is 25 miles ahead of Train Y, how many hours will it be until Train Y is 10 miles ahead of Train X?

Answer 1

3.5 hours.

Explanation:

When train Y is at position 0 train X is at position 25.

Speed = distance / time.

Suppose the distance travelled by train X before Train Y catches up with him is x miles.

Then we have the system

30 = x/ t

40 = (x + 25) / t where t is the time in hours.

x = 30t plug this into the second equation

40 = ( 30t + 25) / t

40t = 30t + 25

10t = 25

t = 2.5 hours.

Now the time taken for train Y to get 10 miles ahead is calculated as follows:

Combined speed = 40 - 30 = 10 mph.

so 10 = 10/t

t = 1 hours.

Answer is 3.5 hours.

Answer 2

3.5 hours

Explanation:

Speed of train X=30 mph

Speed of train Y=40 mph

Relative speed When the two trains travelling in same direction

Relative speed=40-30=10 mph

Total distance =25+10=35 miles

We have to find the time when train Y is 10 miles ahead of train X.

We know that

Time=
`(Distance)/(Relative\;speed)`

Using the formula

Then, we get

Time=
`(35)/(10)=3.5 hours`

Hence, it will be 3.5 hours until train Y is 10 miles ahead of train X.