Question

Greg drove at a constant speed in a rainstorm for 210210 miles. he took aâ break, and the rain stopped he then drove 210210 miles at a speed that was 77 miles per hour faster than his previous speed. if he drove for 1111 âhours, find theâ car's speed for each part of the trip.

Answer 1

Let r and r+7 be Greg's rate for the first and second parts of his trip, respectively. Then:
210/r  + 210/r+7=11
210(r+7)+210r=11(r²+7r)
420r+1470=11r²+77r
11r²-343r-1470=0
(11r+42)(r- 35)=0
r=-42/11 or 35
Choosing the positive value, we get 35 mph as his first speed, and 42 mph as his 2nd speed
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