Question

Two trains move between two towns. It takes the first train 2 hr 48 min and it takes the second 4 hr 40 min. The rate of the first train is 26 mph more thaTwo trains move between two towns. It takes the first train 2 hr 48 min and it takes the second 4 hr 40 min. The rate of the first train is 26 mph more than that of the second train. What is the distance between these towns

Answer 1

182 miles.

Explanation:

Given:

Two trains move between two towns.

Time taken by first train = 2 hr 48 minutes =

Change minute into hour:

60 minute = 1 hour

1 minute =
`(1)/(60)`

48 minutes =
`(1)/(60)*48=(48)/(60) =0.8\ hour`

Time taken by first train in hour =
`2+0.8=2.8\ hours`

Time taken by second train = 4 hr 40 minutes

Similarly, 40 minutes =
`(40)/(60) =0.67\ hour`

Time taken by second train in hour =
`4+0.67=4.67\ hours`

The rate of the first train is 26 mph more than that of the second train.

Question asked:

What is the distance between these towns ?

Solution:

Let speed of second train =
`x\ miles\ per\ hour`

As the speed of the first train is 26 mph more than that of the second train.

Speed of first train =
`26+x\ miles\ per\ hour`

As two trains move between two towns means distance traveled by both train is same.

By using :
`Distance=speed* time`

Distance traveled by first train = Distance traveled by second train

`speed* time` =

`(26+x)2.8=x*4.67`

`26*2.8+x*2.8=4.67x\\72.8+2.8x=4.67x\\`

Subtracting both sides by
`2.8x`

`72.8=1.87x`

Dividing both sides by 1.87

`x=38.93`

Speed of second train = 38.93 miles per hour

`Distance=speed* time`

= 38.93
`*` 4.67

= 181.80 miles.

Thus, the distance between these towns is 182 miles (nearest whole number).