SOLUTION: For the first 4 km of a 10km journey, Jerry and Jerome travelled together at an average speed of x km/h. For the next 6 km, Jerry increased his average speed by 2 km/h while Jerome

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Question 875145: For the first 4 km of a 10km journey, Jerry and Jerome travelled together at an average speed of x km/h. For the next 6 km, Jerry increased his average speed by 2 km/h while Jerome decreased his average speed by 1 km/h.
If the difference in the total time taken to complete the entire journey by Jerry and Jerome is 1.5 hours, find the value of x.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
For the first 4 km of a 10km journey, Jerry and Jerome travelled together at an average speed of x km/h. For the next 6 km, Jerry increased his average speed by 2 km/h while Jerome decreased his average speed by 1 km/h.
If the difference in the total time taken to complete the entire journey by Jerry and Jerome is 1.5 hours, find the value of x.
***
travel time=distance/speed
6%2F%28x-1%29-6%2F%28x%2B2%29=1.5
-6x+6+6x+12=1.5(x-1)(x+2)=1.5(x^2+x-2)
1.5(x^2+x-2)=18
1.5x^2+1.5x-3=18
1.5x^2+1.5x-21=0
x^2+x-14=0
solve for x by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=1, c=-14
ans:
x≈-4.27(reject)
or
x≈3.27