Question

Shelly rode her mountain bike at a rate of 30 km/h for 2.5 h. Josh rode his mountain bike at a rate of 35 km/h for 1 h and then slowed down to 25 km/h for 1.5 h. A) Who travelled farther in 2.5 h? B) What is the difference in the distance travelled by the cyclists?

Answer 1

Part A) Shelly traveled farther in 2.5 h

Part B) The difference in the distance traveled by the cyclists is 2.5 kilometers

Explanation:

Part A) Who traveled farther in 2.5 h?

we know that

The speed is equal to divide the distance by the time

Let

s ----> the speed

d ----> the distance in kilometers

t ----> the time in hours

`s=(d)/(t)`

Solve for d

`d=st`

step 1

Find out the distance traveled by Shelly

we have

`s=30\ km/h\\t=2.5\ h`

substitute the values

`d=30(2.5)=75\ km`

step 2

Find out the distance traveled by Josh

we have

Part 1)

`s_1=35\ km/h\\t_1=1.5\ h`

substitute the values

`d_1=35(1.0)=35\ km`

Part 2)

`s_2=25\ km/h\\t_2=1.5\ h`

substitute the values

`d_2=25(1.5)=37.5\ km`

`d=d_1+d_2`

substitute

`d=35+37.5=72.5\ km`

Compare the distances

`75\ km > 72.5\ km`

so

Shelly traveled farther in 2.5 h

Part B) What is the difference in the distance traveled by the cyclists?

Find out the difference between the two distances

`75\ km-72.5\ km=2.5\ km`