SOLUTION: A tourist starts to walk up a mountain path that is 31 miles long at the rate of 4 miles per hour. After walking for a while, he gets tired and decides to get a taxi. The taxi gets

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Question 1148972: A tourist starts to walk up a mountain path that is 31 miles long at the rate of 4 miles per hour. After walking for a while, he gets tired and decides to get a taxi. The taxi gets him to the top traveling at a constant speed of 50 mph. If the tourist reaches the destination 2 hours after he started, what distance does he have to pay the cab driver for?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x = hours walking at 4mph
Let y = hours riding at 50mph

Then 4x = distance walking
And 50y = distance riding

(1) x+y=2 (the total time was 2 hours)
(2) 4x+50y = 31 (the total distance was 31 miles)

My choice for solving the pair of equations in that form is elimination. Multiply the first equation by 4 and subtract from the second to eliminate x, allowing you to solve for y.
4x+50y = 31
4x+ 4y =  8
-----------
   46y = 23

Finishing from there should be easy....

Answer by ikleyn(52795) About Me  (Show Source):
You can put this solution on YOUR website!
.

            There is another way to solve the problem, using only one unknown. 


Let x be distance traveled by the taxi, in miles.

Then the walking distance is  (31-x) miles.


The time spent by the taxi is  x%2F50  hours.

The time walking is  %2831-x%29%2F4  hours.


The time equation is


    %2831-x%29%2F4 + x%2F50 = 2  hours.


To solve the equation, multiply both sides by 100.  You will get


    25*(31-x)   + 2x = 200

    25*31 - 25x + 2x = 200

    25*31 - 200      = 25x - 2x

    x           = %2825%2A31-200%29%2F23 = 25 km.


ANSWER.  The distance to pay the cab driver for is  25 kilometers.


CHECK.   %2831-25%29%2F4 + 25%2F50 = 6%2F4 + 1%2F2 = 3%2F2 + 1%2F2 = 4%2F2 = 2 hours.   ! Precisely correct !

Solved.

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No one of the two methods is better than the other.

They both are good.

Which one to use, depends on your preferences and methods you use in the class.

But you will benefit, if you know BOTH methods.