Question

Kent drives 270 miles in the same time that it takes Dave to drive 250 miles. If Kent averages 4 miles per hour faster than Dave, find their rates.

Answer 1

Step1: Derive the speed equations from the data.

Given data are as follows

For Dave

Distance traveled = 250 miles

Let the speed of Dave be d miles per hour

For Kent

Distance traveled = 270 miles

Since Kent's speed is 4 miles per hour faster than Dave, we can represent this mathematically

so that If we represent Kent's speed by k. Then

k = 4 + d.

Distance traveled is given by the formula

Distance = Speed x Time

Therefore

`\text{Time}=\frac{Distance}{\text{Speed}}`

So the time spent by Kent is

`\text{time=}\frac{270}{d\text{ +4}}`

The time spent by Dave is

`\text{time}=(250)/(d)`

Step 2: Since they both spend the same time, we will equate their time spent

So

`(270)/(d+4)=(250)/(d)`

Step3: The next step is to solve the above equation

d (270) = 250 (d+4)

Expand the parenthesis

d x 270 = 250 x d + 250 x 4

270d = 250d + 1000

Collect like terms

270d - 250d = 1000

20d = 1000

Divide both sides by 20

d = 1000/20 = 50

d = 50 miles per hour

So Dave's rate is 50 miles per hour

Since we have been told that Kent travels 4 miles per hour faster than Dave, then

Kent = Dave + 4

K = 50 + 4

k= 54 miles per hour

Hence the rates are

Kent = 54 miles per hour

Dave = 50 miles per hour