SOLUTION: Can anyone please help me with this problem? Two motorcycles each make the same 220 mile trip, but one travels 5 mph faster than the other. Find the rates of each motorcycle, if

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Can anyone please help me with this problem? Two motorcycles each make the same 220 mile trip, but one travels 5 mph faster than the other. Find the rates of each motorcycle, if      Log On


   

Question 81406: Can anyone please help me with this problem?
Two motorcycles each make the same 220 mile trip, but one travels 5 mph faster than the other. Find the rates of each motorcycle, if the slower one takes 24 minutes longer to complete the trip than the faster one. Show set-up, and equation work.
Thanks.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
distance=rate X time ... let r=rate of slower motorcycle ... let t=time of faster motorcycle (in hours)

for slower ... 220=r*(t+.4) ... t=(220/r)-.4 ... (24 min=.4 hr)

for faster ... 220=(r+5)*t ... substituting t from slower gives ... 220=(r+5)*((220/r)-.4)

FOILing gives 220=220-.4r+(1100/r)-2 ... 0=-.4r-2+(1100/r) ... multiplying by r gives 0=-.4r%5E2-2r%2B1100

dividing by -.4 gives 0=r%5E2%2B5r-2750 ... using quadratic formula gives r=%28-5+%2B-+sqrt%2811025%29%29%2F2

r=-55 and r=50 ... the negative value is unrealistic ... so slower=50 and faster=55