Question

Bill is planning to drive 280 km. If he were to start his trip 1 hour later than he plans, he would need to drive 10 miles/hour faster to make the trip in the same amount of time. What is the average speed at which Bill plans to drive?

Answer 1

Average speed was `48.15` miles/hour (approx.)

Explanation:

Let `t` be the amount of time (in hours) required to travel `280` miles at the speed `s` (in miles per hour).
`color(white)("XXX")rarr t=280/s`

We told it would take `(t-1)` hours to travel the `280` miles at a speed of `(s+10)` miles per hour.

Therefore
`color(white)("XXX")(t-1) * (s+10)= 280`

...and replacing `t` with `(280/s)` from our initial equation:
`color(white)("XXX")(280/s-1) * (s+10) = 280`

Simplifying
`color(white)("XXX")280+2800/s-s-10 = 280`

`color(white)("XXX")2800/s-s-10=0`

multiplying by `(-s)` and re-arranging into standard form:
`color(white)("XXX")s^2+10s-2800=0`

Applying the quadratic formula (but ignoring the theoretically negative result)
`color(white)("XXX")s=(-10+sqrt(10^2-4 * 1 * (-2800)))/(2 * 1)`

`color(white)("XXX")~~48.15072906` (using calculator)