SOLUTION: Bob and Moe set off at the same time on a 30km walk for charity. Bob who has trained all year for this event, walks 1.4km/h faster than Moe, but sees a friend en route and stops t

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Question 32318: Bob and Moe set off at the same time on a 30km walk for charity. Bob who has trained all year for this event, walks 1.4km/h faster than Moe, but sees a friend en route and stops to talk for 20 min. Even with this delay, Bob finished the walk 2 hours ahead of Moe. How fast was each person walking, and how long did it take for each person to finish the walk?
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the rate for Moe be x
Let the rate for Bob be 1.4+x
Bob's partial time = 2 hours and 20 minuts (1/3 hours) or 7/3 hours:
Equation:
30%2F%281.4%2Bx%29-30%2Fx=7%2F3--->Multiply the whole equation by 3 to remove the fraction:
90%2F%281.4%2Bx%29-90%2Fx=7
90[(1.4+x)-(x)]=7[(1.4+x)(x)]}}}
126=7%281.4x%2Bx%5E2%29
7x%5E2%2B9.8x-126=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=7, b=9.8, c=-126

SImplfy:
x=3.6
3.6+1.4=5
Total time for each: -->30/(5)=6 and 30/3.6=8.33
Hence, Bob's rate is 5kmph with 6 hours of total, and Moe's rate is 3.6kmph with 8.33 hours of total.
Paul.