SOLUTION: Wanatobe walked to the moot at 4 miles per hour and then rode back home in bus at 24 miles per hour. If her total traveling time was 14 hours, how far was it to the moot?

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Question 1202282: Wanatobe walked to the moot at 4 miles per hour and then rode back home in bus at 24 miles per hour. If her total traveling time was 14 hours, how far was it to the moot?
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52865) About Me  (Show Source):
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.
Wanatobe walked to the moot at 4 miles per hour and then rode back home
in bus at 24 miles per hour. If her total traveling time was 14 hours,
how far was it to the moot?
~~~~~~~~~~~~~~~~~~ 

Let x be the one-way distance, in miles.


The time spent walking is  x%2F4  hours.

The time spent by bus is  x%2F24.


The total time equation is

    x%2F4 + x%2F24 = 14  hours.


It is your basic equation to solve and to find x.


To solve it, multiply both sides of the equation by 24.  You will get

    6x + x = 14*24

      7x   = 14*24

       x   =  2*24 = 48.


ANSWER.  One way distance is 48 miles.


CHECK.  The time walking = 48/4 = 12 hours.

        The time by bus = 48/24 = 2 hours.

        Total time 12 + 2 = 14 hours.  ! correct !

Solved.



Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


The distances there and back are the same, so the ratio of times at the two speeds is the same as the ratio of the two speeds.

The ratio of the two speeds is 4:24 = 1:6, so the ratio of the times at the two speeds is 6:1.

14 hours total, divided in the ratio 6:1, means 12 hours at the lower speed of 4 mph and 2 hours at the higher speed of 24 mph.

12 hours at 4 mph makes the distance 12*4 = 48 miles; and 2 hours at 24 mph makes the distance 2*24 = 48 miles.

ANSWER: 48 miles

Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
Speeds going to moot, G
Speed coming back from moot, R
Total roundrip time T
distance to moot, d 
             SPEEDS         TIMES         DISTANCE

TO MOOT        G             d/G              d

RETURN         R             d/R              d

TOTAL                          T

d%2FG%2Bd%2FR=T
d%281%2FG%2B1%2FR%29=T
d%28%28R%2BG%29%2F%28GR%29%29=T
highlight%28d=T%28%28GR%29%2F%28R%2BG%29%29%29
Substitute your given values.

G=4
R=24
T=14
evaluate d.