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?

1 Answer
Alan P.
Nov 10, 2016

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)

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