SOLUTION: An automobile averaged 40 mph for part of a trip and 50 mph for the remainder. If the 5-hour trip covered 210 miles, for how long did the car average 40 mph?

Question 179158: An automobile averaged 40 mph for part of a trip and 50 mph for the remainder. If the 5-hour trip covered 210 miles, for how long did the car average 40 mph?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Distance(d)=Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let d=distance travelled at 40 mph
Then (210-d)=distance travelled at 50 mph
time travelling at 40 mph=d/40
time travelling at 50 mph=(210-d)/50
Now we are told that the above two times=5 hr, so:
d/40 +(210-d)/50=5 multiply each term by 200
5d +4(210-d)=1000 get rid of parens
5d+840-4d=1000 subtract 840 from each side
5d+840-840-4d=1000-840 collect like terms
d=160 mi distance travelled at 40 mph
Time travelled at 40 mph=160/40=4 hr----------------------ans
CK
40*4+50*1=210
210=210

Hope this helps---ptaylor
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