Question

Two kids at a summer camp, Diego and Shontal, are competing in a potato sack race. Diego is younger, so he is given a head start of 27 yards. When the race starts, Diego hops at a rate of 2 yards per second, and Shontal hops 3 yards per second. Eventually, Shontal will overtake Diego. How far will Shontal have to hop? How long will that take?

Answer 1

Answer:

(a)81 yards (b)27 seconds

Step-by-step explanation:

Let Shontal distance to the point where he overtakes Diego=x

Since Diego is given a head start of 27 yards, his distance to the point where he is overtaken by Shontal=x-27

Diego hops at a rate of 2 yards per second.

Shontal hops 3 yards per second.

Now, Time Taken=Distance ÷ Average Speed

• For Diego, Time Taken = (x-27) ÷ 2
• For Shontal, Time taken = x ÷ 3

At the point where Shontal overtakes Diego, their time taken are equal.

Therefore:

$\frac{x-27}{2}=\frac{x}{3}$

Cross multiplying

3(x-27)=2x

3x-81=2x

3x-2x=81

x=81 yards

(a) Therefore, Shontal will have to hop 81 yards

(b)Recall, for Shontal,

Time taken = x ÷ 3 = 81 ÷ 3 =27 seconds

It will take Shontal 27 seconds to overtake Diego.