SOLUTION: a candy truck leaves the store at 5:00 am each mornng on its 144 mile route.one day the driver gets a late start and does not leave the store until 5:30 am. to finish his route on

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Question 722710: a candy truck leaves the store at 5:00 am each mornng on its 144 mile route.one day the driver gets a late start and does not leave the store until 5:30 am. to finish his route on time the driver drives 4 miles per hour faster than usual.at what speed does he usually drive ?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
normal speed r in miles per hour. The difference between 5:00am and 5:30am is 1/2 hour.

____________speed________________time____________________distance
normal_______r___________________t=144%2Fr_______________________144
late________r+4__________________t-1%2F2=144%2F%28r%2B4%29___________________144

The normal time being 1/2 hour more than the late time suggests taking the difference between their expressions. Both expressions may be shown as expressions using r, the rate.

normal time minus late time equals 1/2 hour,
highlight%28144%2Fr-144%2F%28r%2B4%29=1%2F2%29.
Multiply left side and right side by 2r%28r%2B4%29 to clear the fractions.
288%28r%2B4%29-288r=r%28r%2B4%29
288r%2B1152-288r=r%5E2%2B4r
1152=r%5E2%2B4r
highlight%28r%5E2%2B4r-1152=0%29, .


r=%28-4%2Bsqrt%2816-4%2A%28-1152%29%29%29%2F2=%2868-4%29%2F2
=32 miles per hour --- ANSWER.