Question

Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 252 miles in the same time that Dana travels 228 miles. If Chuck's rate of travel is 6 mph more than Dana's, then at what rate does Chuck travel?

Answer 1

63 m/h

Explanation:

Chuck travels 252 miles and Dana travels 228 miles. Their rates of travel (speeds) differ by 6 mph. Chuck travels faster.

Let us assume Dana's speed to be
`x(m)/(h)`. Then Chuck's speed is
`(x+6)(m)/(h)`.

Now, their times of travel are the same.

`Speed=\frac{Distance}{\textrm{Time Taken}}`

`\textrm{Time Taken = }(Distance)/(Speed)`

`(252m)/(x+6(m)/(h) )=(228m)/(x(m)/(h) )`

`(x+6)/(x)=(252)/(228)`

`(6)/(x)=(252)/(228)-1=0.10526`

`x=(6)/(0.10526)=57(m)/(h)`

∴ Chuck's rate of travel =
`x+6=57+6=63(m)/(h)`

Answer 2

Chuck's rate of travel = 63mph

Explanation:

Given chuck travels 252 miles and dana travels 228 miles. Given that they both take same time to travel .

Let the travelling time be T.

Also given that the speed of chuck is 6mph greater than that of dana's.

let the speed of chuck be x. Now

Speed =
`(distance )/(time)`

x=
`(252)/(T)`

Now for Dana's speed

x-6=
`(228)/(T)`

When we divide both the equations we get

`(x)/(x-6)=(252)/(228)`

`(x)/(x-6)=(63)/(57)`

x=63mph