Question

Starting at home, Ishaan traveled uphill to the gift store for 18 minutes at just 10 mph. He then traveled back home along the same path downhill at a speed of 30 mph. What is his average speed for the entire trip from home to the gift store and back?

Answer 1

Answer: $\text{The average speed for the entire trip from home to the gift store and back}=15\text{ mph}$

Step-by-step explanation:

Time taken to travel from uphill to the gift store =18 minutes

∴ $t_1=18\ minutes=\frac{18}{60}\ hour=0.3\ hour$

Speed of Ishaan from uphill to the gift store =10 mph

We know that $\text{Distance}=\text{Speed}\times\text{time}$

$\\\Rightarrow\d_1=10\times0.3=3\ \text{miles}$

We he traveled back, the distance remains same

Thus $d_2=d_1=3\text{ miles}$

We know that

$\text{time}=\frac{\text{Distance}}{\text{speed}}\\\Rightarrow\ t_2=\frac{3}{30}=0.1\text{ hour}$

$\text{The average speed}=\frac{\text{total distance}}{\text{total time}}\\=\frac{3+3}{0.3+0.1}\\\\=\frac{6}{0.4}\\\\=\frac{60}{4}=15\\\\\Rightarrow\text{The average speed}=15\text{ mph}$

$\text{The average speed for the entire trip from home to the gift store and back}=15\text{ mph}$

Answer 2

The answer would be 15 miles per hour.