SOLUTION: John and Mary are 300m apart on a straight road. They run at uniform speed. If they run towards each other, they will meet in 30 seconds. If they run in the same direction, John wi
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Question 808615: John and Mary are 300m apart on a straight road. They run at uniform speed. If they run towards each other, they will meet in 30 seconds. If they run in the same direction, John will overtake Mary in 70 seconds. Find their speeds of running.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
John and Mary are 300m apart on a straight road.
They run at uniform speed.
If they run towards each other, they will meet in 30 seconds.
If they run in the same direction, John will overtake Mary in 70 seconds.
Find their speeds of running.
:
let j = John's speed
let m = Mary's speed
:
Write a distance equation for each scenario
30(j + m) = 300; toward each other
70(j - m) = 300; same direction
:
30j + 30m = 300
70j - 70m = 300
multiply the 1st equation by 7, multiply the 2nd equation by 3
210j + 210m = 2100
210j - 210m = 900
-------------------adding eliminates m , find j
420j = 3000
j = 3000/420
j = 7.143 m/sec is John's speed
:
Find m
30(7.143) + 30m = 300
214.3 + 30m = 300
30m = 300 - 214,.3
30m = 85.7
m = 85.7/30
m = 2.857 m/sec is Mary's speed
:
:
Check this in the 2nd equation
70(7.143-2.857) =
70(4.386) = 300
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