SOLUTION: Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race. During your run, your average speed is 6 miles per hour, and during your bicycle race,

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Question 1209001: Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race. During your run, your average speed is 6 miles per hour, and during your bicycle race, your average speed is 25 miles per hour. You finish the race in 5 hours. What is the distance of the run? What is the distance of the bicycle race?
Found 4 solutions by josgarithmetic, ikleyn, timofer, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
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RATE%2ATIME=DISTANCE

DISTANCE%2FSPEED=TIME
                SPEED           TIME          DISTANCE
RUN               6             x/6                x
BICYCLE          25             (87-x)/25        87-x
TOTAL                            5               87

Equation to solve is x%2F6%2B%2887-x%29%2F25=5.

Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race.
During your run, your average speed is 6 miles per hour, and during your bicycle race,
your average speed is 25 miles per hour. You finish the race in 5 hours.
What is the distance of the run? What is the distance of the bicycle race?
~~~~~~~~~~~~~~~~~~~~ 

Let "t" be the time running, in hours.

Then the time cycling is (5-t) hours.


The total distance equation is 

    6t + 25(5-t) = 87  miles.


Simplify and find "t"

    6t + 125 - 25t = 87,

     125 - 87 = 25t - 6t

         38   =    19t

          t    =    38/19 = 2 hours.


So, you run 2 hours and cycle 5-2 = 3 hours.


The distance running is  6*2 = 12 miles.  The distance cycling is 25*3 = 75 miles.    ANSWER

Solved.



Answer by timofer(106) About Me  (Show Source):
You can put this solution on YOUR website!
If using RT=D rule then also T=D/R.

If letting x equal to distance done by running then
x%2F6%2B%2887-x%29%2F25=5
common denominator is 150.
150%28x%2F6%2B%2887-x%29%2F25%29=150%2A5
25x%2B6%2A87-6x=750
%2825-6%29x=750-522
19x=750-522
x=228%2F19
x=12----------the distance ran

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a VERY different approach to solving the problem than the standard algebraic method shown by the other tutors.

Your average speed running is 6 mph; your average speed cycling is 25 mph.

Your overall average speed is 87/5 = 17.4 mph.

Use a number line if it helps to observe/calculate that 17.4 is 3/5 of the way from 6 to 25. That means 3/5 of the total time was at the higher speed.

The total time was 5 hours, and 3/5 of the time, or 3 hours, was at the higher speed.

So your cycling time was 3 hours and your running time was 2 hours.

The cycling distance, 3 hours at 25 mph, was 3*25 = 75 miles.

The running distance, 2 hours at 6 mph, was 2*6 = 12 miles.

ANSWERS:
running distance: 12 miles
cycling distance: 75 miles