Question 939988: Systems of linear equations
James and George are both cycling on the same road. They are currently 21 miles apart. If the two cyclists bike towards eachother, they will pass each other in 36 minutes. If they cycle in the same direction, James will pass George in 7 hours. Find the average rate if speed, in miles per hour, of both cyclists.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! James and George are both cycling on the same road.
They are currently 21 miles apart.
If the two cyclists bike towards each other, they will pass each other in 36 minutes.
If they cycle in the same direction, James will pass George in 7 hours.
Find the average rate if speed, in miles per hour, of both cyclists.
:
change 36 min to hrs: 36/60 = .6 hrs
:
let j = J's speed
let g = G's speed
:
Write a distance equation for each scenario, dist = time * speed
:
.6(j + g) = 21; (towards each other, their speeds are additive)
7(j - g) = 21; (going the same direction, you subtract their speeds)
:
We can simplify both these equations, divide the first by .6, divide the 2nd by 7.
j + g = 35
j - g = 3
-------------adding eliminates g, find j
2j = 38
j = 38/2
j = 19 mph is J's speed
:
Use the equation j + g = 35, to find g
19 + g = 35
g = 35 - 19
g = 16 mph is G's speed
;
:
Check solution in the 1st original equation
.6(19 + 16) = 21
.6(35) = 21
You can check it in the 2nd original equation
|
|
|
