Chapter 14, Problem 43CCSR

Solution

To find: The speed of a train.

The speed of a train is 30 mi/h, that is, option (F) is correct.

Given information: The speed of a car is 15 mi/h faster than the speed of a train. Also, the car and train are 150 m apart after 2 hours.

Concept used:

The relation between speed, distance, and time is $\text{distance}=\text{speed}\times \text{time}$ .

Calculation:

Consider the speed of the train as $x\text{ mi/h}$ .

So, according to the given statement, the speed of a car is $\left(x+15\right)\text{mi/h}$ .

According to the relation between speed, distance, and time, the distance travelled by train and car in 2 h is $2x\text{ mi}$ and $2\left(x+15\right)\text{mi/h}$ , respectively.

So, equate the sum of distances travelled by car and train to 150 and solve for $x$ .

  $\begin{array}{c}2x+2\left(x+15\right)=150\\ 2x+2x+30=150\\ 4x+30=150\\ 4x=120\\ x=30\end{array}$

So, the speed of the train as $\text{30 mi/h}$ .

Hence, option (F) is correct.