Question

Simran drove 40 miles to see her cousin and at 20 mph. The trip took Simran 2 hours. Then, Simran drove from her cousin’s house and drove another 30 miles to the store at a speed of 10 mph. It took Simran 3 hours to arrive at the store. What was Simran’s average speed for the trip?
A. 14 mph
B. 16 mph
C. 18 mph
D. 12 mph

Answer 1

Hint: First we will calculate the total distance travelled by Simran from her starting point to her cousin’s house and from her cousin’s house to store. Similarly, we calculate the total time taken to complete her trip. Then, by using the formula we calculate the average speed of the Simran. The formula of average speed used will be $\text{Average speed=}\dfrac{\text{Total distance travelled}}{\text{Total time taken}}$

Complete step-by-step answer:
We have been given that Simran drove 40 miles to see her cousin and at 20 mph. The trip took Simran 2 hours. Then, Simran drove from her cousin’s house and drove another 30 miles to the store at a speed of 10 mph. It took Simran 3 hours to arrive at the store.
We have to find Simran's average speed for the trip.
Now, let us calculate the total distance travelled by Simran.
Total distance will be $\text{Distance travelled from her starting point to her cousin }\!\!'\!\!\text{ s house + her cousin }\!\!'\!\!\text{ s house to store}$
$\begin{align}
  & \text{Total distance = 40+30} \\
 & \text{Total distance = 70 miles} \\
\end{align}$
Now, total time taken to complete the trip will be
$\text{Time taken to reach at her cousin }\!\!'\!\!\text{ s house + her cousin }\!\!'\!\!\text{ s house to store}$
$\begin{align}
  & \text{Total time taken = 2+3} \\
 & \text{Total time taken = 5 hours} \\
\end{align}$
Now, we know that $\text{Average speed=}\dfrac{\text{Total distance travelled}}{\text{Total time taken}}$
Substituting the values, we get
$\begin{align}
  & \text{Average speed=}\dfrac{70}{5} \\
 & \text{Average speed =14 mph} \\
\end{align}$
So, we get the average speed for the trip is $\text{14 mph}$.

So, the correct answer is “Option A”.

Note: If students try to solve the question directly as the speeds are given as 20 mph and 30 mph, so the average speed will be $\dfrac{20+30}{2}=\dfrac{50}{2}=25$ mph but it is a wrong answer. So, it is necessary that students have a clear idea of the concept of average speed.