SOLUTION: In a first race, A gives b a Headstart of 100 feet and overtakes him in four minutes. In the second race he gains 750 feet on B when B runs 9000 feet. Find the rate at which each r
Algebra.Com
Question 893076: In a first race, A gives b a Headstart of 100 feet and overtakes him in four minutes. In the second race he gains 750 feet on B when B runs 9000 feet. Find the rate at which each runs.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Call the runners A and B
Let their speeds be and in feet / minute
-----------------------
Start a stopwatch when A leaves
In the 1st race:
Let = the distance A runs when he overtakes B
A's equation:
(1)
B's equation:
(2)
================
In the 2nd race:
I think they both leave at the same time, so
Let = time in minutes until A is ft
ahead of B
------------------
A's equation:
(3)
B's equation:
(4)
-------------------
This is actually 4 equations with 4 unknowns,
so it is solvable
Substitute (1) into (2)
(2)
(2)
(2)
(2)
-----------------------
Substitute (4) into (3)
(4)
(3)
(3)
(3)
Divide both sides by
(3)
Substitute (2) int (3)
(3)
(3)
(3)
and, since
(2)
(2)
-----------------
A's speed is 325 ft/min
B's speed is 300 ft/min
---------------------
check:
(1)
(1)
(1) ft
and
(2)
(2)
(2)
(2) ft
OK
You can check (3) and (4)
RELATED QUESTIONS
A turtle and a rabbit are in a race to
see who is first to reach a point
100 feet... (answered by addingup,MathTherapy)
Albert and Bob ran a race of 440 yards. In the first trial, Albert gave Bob a headstart... (answered by ankor@dixie-net.com)
A race car travels 100 feet in .5 seconds. At this rate of speed, how far will the race... (answered by Cromlix)
A turtle and a rabbit are in a race to see who is first to reach a point 100 feet away.... (answered by ankor@dixie-net.com)
A and B run a distance of 2 kms two time. first A finishes the race 2 minutes before B.... (answered by ankor@dixie-net.com)
1a.Stella is having a race with Tess. Stella gives Tess a 5o foot head start. Stella... (answered by stanbon)
the amount of time it takes a swimmer to swim a race is inversely proportional to the... (answered by mananth,stanbon)
Solve. The amount of time it takes a swimmer to swim a race is inversely proportional to... (answered by ewatrrr)
The amount of time it takes a swimmer to swim a race is inversely proportional to the... (answered by mananth,josgarithmetic,Boreal,greenestamps)