Question

Set up an equation and solve the following problem.

Kent drives 230 miles in the same time that it takes Dave to drive 210 miles. If Kent averages 4 miles per hour faster than Dave, find their rates.
Dave mph
Kent mph

Answer 1

The speed of Dave is 42 miles per hour

The speed of Kent is 46 miles per hour .

Explanation:

Given as :

The distance cover by Dave = d = 210 miles

The time taken by Dave = t hour

The speed of Dave = s miph

Again

The distance cover by Kent = D = 230 miles

The time taken by Kent = T hour

The speed of Kent = S = (s + 4 ) miph

For Dave

Time =
`(\textrm Distance)/(\textrm Speed)`

So, t =
`(\textrm d miles)/(\textrm s miph)`

Or, t =
`(\textrm 210 miles)/(\textrm s miph)`

For Kent

Time =
`(\textrm Distance)/(\textrm Speed)`

So, T =
`(\textrm D miles)/(\textrm S miph)`

Or, T =
`(\textrm 230 miles)/(\textrm (s + 4) miph)`

∵ Time taken by both is same

So, t = T

Or,
`(\textrm 210 miles)/(\textrm s miph)` =
`(\textrm 230 miles)/(\textrm (s + 4) miph)`

Or, 210 × (s + 4) = 230 × s

Or, 210 × s + 210 × 4 = 230 × s

Or, 210 × 4 = 230 × s -210 × s

Or, 210 × 4 = 20 × s

∴ s =
`(840)/(20)`

i.e s = 42 miph

So, The speed of Dave = s = 42 miles per hour

Again

The speed of Kent = S = (s + 4 ) miph

i.e S = 42 + 4

or, S = 46 miph

So, The speed of Kent = S = 46 miles per hour

Hence,The speed of Dave is 42 miles per hour

And The speed of Kent is 46 miles per hour . Answer