Question 12570: This is the question: Mr. Smith was told by his doctor that he needed to excercise. On Monday he jogged for 2 hours and then walked 3 hours to cover 30 miles in total. On Tuesday he jogged for 2.5 hours and then walked 4 hours to cover 38.5 miles in total. Find his speed (in miles per hour) when he is jogging.(please help me!)
Answer by AdolphousC(70)   (Show Source):
You can put this solution on YOUR website! This is a system of equations problem, so you need to define your variables,
Let J = Miles per hour while jogging, and W equal miles per hour while walking.
Now set up your two equations, your first equation will be
2J + 3W = 30
and your second equation will be
2.5J + 4W = 38.5
Now you need to find a common coefficient, I am going to turn the coefficients for W into 12 by multiplying the top equation by 4 and the bottom one by 3.
4( 2J + 3W = 30 )
3( 2.5J + 4W = 38.5 )
Now you need to multiply, and you get
8J + 12W = 120
7.5J + 12W = 115.5
Subtract the two equations
0.5J = 4.5
Divide by 0.5
J = 9
Which means she Jogs at 9MPH
Now go back and substitue 9 for J and solve for W
using the first equation ( 2J + 3W = 30 )
2(9) + 3W = 30 Multiply
18 + 3W = 30 Subtract
3W = 12 Divide
W = 4
So she can walk 4 MPH
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