Question

st 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

Answer:

182 miles.

Step-by-step 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 = $\frac{1}{60}$

48 minutes = $\frac{1}{60}\times48=\frac{48}{60} =0.8\ hour$

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 = $\frac{40}{60} =0.67\ hour$

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 : $Distance=speed\times time$

Distance traveled by first train = Distance traveled by second train

$speed\times time$ =

$(26+x)2.8=x\times4.67$

$26\times2.8+x\times2.8=4.67x\\72.8+2.8x=4.67x$

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

$Distance=speed\times time$

              = 38.93 $\times$ 4.67

              = 181.80 miles.

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