SOLUTION: A TRUCK DRIVER TRAVELED AT 40mph for the first part of a 646-miletrip, then increased his speed to 58 mph for the rest of the trip. the entire trip took 13 hours. how many hours ar

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Question 518399: A TRUCK DRIVER TRAVELED AT 40mph for the first part of a 646-miletrip, then increased his speed to 58 mph for the rest of the trip. the entire trip took 13 hours. how many hours are traveled at 58 mph?
Found 2 solutions by Alan3354, Maths68:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A TRUCK DRIVER TRAVELED AT 40mph for the first part of a 646-miletrip, then increased his speed to 58 mph for the rest of the trip. the entire trip took 13 hours. how many hours are traveled at 58 mph?
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d = distance at 58 mi/hr
d/58 + (646-d)/40 = 13
Multiply by 58*40
40d + 58*(646-d) = 13*40*58 = 30160
40d - 58d + 37468 = 30160
-18d = -7308
d = 406 miles
406 mi/58 mi/hr = 7 hours

Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
Let
He Drove at 40mph = t hours
He Drove at 58mph = 13-t hours
Distance he covered at 40mph = 40t
Distance he covered at 50mph = 50(13-t)
Total Distance covered = 646

Distance he covered at 40mph + Distance he covered at 50mph = Total Distance covered
40t+50(13-t)=646
40t+650-50t=646
40t-50t=646-650
-10t=-4
-10t/t=-4/-10
t=4/10
t=2/5
He Drove at 40mph = t = 2/5 hours or 24 minutes
He Drove at 58mph = 13-t = 13-(2/5)=(65-2)/5=63/5= 5hours 3/5 minutes (36 minutes)
Check
======
Distance he covered at 40mph = 40t = 40 * 2/5 = 8*2=16 miles
Distance he covered at 50mph = 50 * 63/5 = 10*63=630 miles
Sum both distances = 16+630=646 miles