Question 1031863: frank went 16 miles at one speed and then caame back going 4mph faster. if the return trip took 40mins less time find the 2 speeds. Found 4 solutions by mananth, ikleyn, n2, josgarithmetic:Answer by mananth(16949) (Show Source):
You can put this solution on YOUR website! Forward time - return time = 40 minutes = 2/3 hours
Let forward rate be x
return rate = x+4
16/x - 16/(x+4) = 2/3
LCD
3x(x+4)
48(x+4) -48x = 2*3x(x+4)
48x + 192 -48x = 6x^2+24x
6x^22 +24x -192=0
/6
x^2+4x-32=0
x^2+8x-4x-32=0
x(x+8)-4(x+8) =0
(x+8)(x-4) =0
x=4 the positive value
4 mph & 8 mph
You can put this solution on YOUR website! .
frank went 16 miles at one speed and then came back going 4mph faster. if the return trip took 40 mins
less time find the 2 speeds.
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The solution in the post by @mananth is incorrect.
It has an arithmetic error on the way, which leads to wrong answer.
I came to bring a correct solution.
Let x be the rate going to there, in miles per hour.
Then the rate going back is (x+4) miler per hour.
The time going at one speed is hours.
The time going back is hours.
The time equation is
- = .
To solve, multiply both sides by LCD 3x*(x+4). You will get
48(x+4) - 48x = 2x(x+4) <<<---=== note it is DIFFERENT equation than that in the post by @mananth
192 = 2x(x+4)
96 = x(x+4)
x^2 + 4x - 96 = 0
(x+12)*(x-8) = 0
The roots are -12 and 8. We reject negative root and accept the positive one x = 8.
ANSWER. The speeds are 8 mph (going to there) and 12 mph (going back).
CHECK. The time going to there is = 2 hours.
The time going back is = = = 1 hours.
The difference is of an hour, which is PRECISELY CORRECT.
You can put this solution on YOUR website! .
frank went 16 miles at one speed and then came back going 4mph faster. if the return trip took 40 mins
less time find the 2 speeds.
~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let x be the rate going to there, in miles per hour.
Then the rate going back is (x+4) miler per hour.
The time going at one speed is hours.
The time going back is hours.
The time equation is
- = .
To solve, multiply both sides by LCD 3x*(x+4). You will get
48(x+4) - 48x = 2x(x+4)
192 = 2x(x+4)
96 = x(x+4)
x^2 + 4x - 96 = 0
(x+12)*(x-8) = 0
The roots are -12 and 8. We reject negative root and accept the positive one x = 8.
ANSWER. The speeds are 8 mph (going to there) and 12 mph (going back).
CHECK. The time going to there is = 2 hours.
The time going back is = = = 1 hours.
The difference is of an hour, which is PRECISELY CORRECT.
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