SOLUTION: Each day, Amit runs nine miles and then walks one mile. He runs 10 mph faster than he walks. If his total time is 75 minutes, then what is Amit's running speed?

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Question 282326: Each day, Amit runs nine miles and then walks one mile. He runs 10 mph faster than he walks. If his total time is 75 minutes, then what is Amit's running speed?
Found 4 solutions by mananth, ikleyn, josgarithmetic, MathTherapy:
Answer by mananth(16949)   (Show Source):
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Each day, Amit runs nine miles and then walks one mile. He runs 10 mph faster than he walks. If his total time is 75 minutes, then what is Amit's running speed?
let him walk at x mph
he runs x+10 mph
time taken for running = 9/x+10
time he walks = 1/x
1/x+ 9/ x+10= 5/4 hours
x+10 +9x / x(x+10) = 5/4
10x+10= 5x(x+10) / 4
10x+10 = 5x^2 +50x /4
40x+40 = 5x^2 +50x
5x^2-10x-40=0
x^2-2x-8=0
x^2-4x +2x-8=0
x(x-4)+2(x-4)=0
(x+2)(x-4)=0
So x =4 mph walking speed
Running speed will be x+10 = 4+10 = 14 mph

Answer by ikleyn(53742)   (Show Source):
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.
Each day, Amit runs nine miles and then walks one mile. He runs 10 mph faster than he walks.
If his total time is 75 minutes, then what is Amit's running speed?
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        The solution and the answer in the post by @mananth both are incorrect due to arithmetic errors on the way.
        I came to bring a correct solution.

let him walk at x mph he runs x+10 mph time taken for running = 9/x+10 time he walks = 1/x Time equation 1/x + 9/(x+10) = 5/4 hours Simplify and find x 4(x+10) + 36x = 5x(x+10) 4x + 40 + 36x = 5x^2 + 50x 40x + 40 = 5x^2 + 50x 5x^2 + 10x - 40 = 0 x^2 + 2x - 8 = 0 (x+4)*(x-2) = 0. The roots are x= -4 and x= 2. Since we look for the speed, we accept the positive root x= 2 and reject the negative one. ANSWER. Amit's walking speed is 2 miles per hour and his running speed is 2+10 = 12 mph. CHECK for the travel time. = = = of an hour. ! precisely correct !

Solved correctly.

Answer by josgarithmetic(39790)   (Show Source):
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Seventy-five minutes is one and quarter hours.

SPEED TIME DISTANCE WALK r-10 1/(r-10) 1 RUN r 9/r 9 SUM 1.25

Answer by MathTherapy(10801)   (Show Source):
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Each day, Amit runs nine miles and then walks one mile. He runs 10 mph faster than he walks. If his total time is 75 minutes, then what is Amit's running speed? ******************************************************************* Let Amit's running-speed be S Since his running-speed is 10 mph faster than his walking-speed, then Amit's walking-speed is "S - 10" mph With his running distance being 9 miles, Amit's time to run these 9 miles is And, with his walking distance being 1 mile, Amit's time to cover this mile is It's stated that Amit's total time to run and walk "....is 75 minutes," or . This gives us the following total TIME equation: , with S > 10 9(4)(S - 10) + 4S = 5S(S - 10) --- Multiplying by LCD, 4S(S - 10) (S - 12)(S - 6) = 0 S - 12 = 0 or S - 6 = 0 ----- Setting FACTORS equal to 0 S = 12 mph or 6 mph. However, 6 is NOT > 10 (see above constraint). So, Amit's running-speed is 12 mph