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
Nov 10, 2016

Answer:

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)