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sladkih [1.3K]
2 years ago
7

You and a friend are running on treadmills. you run 0.5 mile every 3 minutes and your friend runs 2 miles every 14 minutes. you

both start and stop running at the same time and run a whole number of miles. what is the least possible number of miles you and your friend can run?
Mathematics
2 answers:
Natali5045456 [20]2 years ago
4 0
I run 1 mile every 6 minutes.
My friend runs 1 mile every 7 minutes.
Lowest Common Multiple:  LCM ( 6, 7 ) = 42 minutes.
Me : 42 : 6 = 7 miles
My friend : 42 : 7 = 6 miles. 

rosijanka [135]2 years ago
4 0
Start by finding how long it takes each to run 1 mile.

You: 0.5 mile every 3 minutes => 1 mile every 6 minutes

Your friend 2 miles every 14 minutes => 1 mile every 7 minutes

Now you have to calculate the minimum common multiple of 6 and 7.

For that you need to factor both numbers and take common and non common factors raised to their highest exponent:

6 = 3*2
7 = 7

Then the minimum common multiple is 2*3*7=42.

Now divide the time 42 by the humber of minutes each of you take to run 1 mile

you: 42 minutes / 6 minutes per mile = 7 miles
your friend 42 minutes / 7 minutes per mile = 6 miles.

You can run 7 miles and your friend 6 miles in the same time.

Answer: 7 and 6

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The values of (x,y)=(4,4). In terms of x, the value y(x)=8-x, If the given equation is x-y=0 and x+y=8.

Step-by-step explanation:

The given is,

                              x-y=0...............................(1)

                              x+y=8...............................(2)

Step:1

          Solution can be obtained by Elimination method,

          Equation (1) is multiplied by (-1)           ( Eqn (1) × -1 )

                             -x+y=0..............................(3)

          Substrate the equation (1) and equation (3),

                              -x+y=0

                                x+y=8

         ( - )

         (-x-x)+(y-y)=(0-8)

                             (-2x)=-8

                                -2x = -8

         we can cancel the minus because it is available in both sides,

                                  2x=8

                                    x = \frac{8}{2}

                                     x = 4

        From the value of x, Equation (2) becomes,

                              x+y=8

                               4+y=8

                                     y = 8-x    (Value of y in terms of x)

        Where, x = 4

                                     y = 8-4        

                                     y =4

Step:2

       Check for solution,

                             x+y=8.....................................(2)

       Substitute the values of x and y,

                             4 + 4 = 8

                                   8 = 8

Result:

         The values of (x,y)=(4,4). In terms of x, the value y(x)=8-x, where x=4. If the given equation is x-y=0 and x+y=8.

         

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