SOLUTION: Ahmed can run a steady pace of 5m/s and Abdullah can only run at 4 m/s. Ahmed allows Abdullah a 15m headstart in a 100m race. How far from the starting line will Ahmed overtake Abd
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Question 1136630: Ahmed can run a steady pace of 5m/s and Abdullah can only run at 4 m/s. Ahmed allows Abdullah a 15m headstart in a 100m race. How far from the starting line will Ahmed overtake Abdullah? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52787) (Show Source):
Let " d " be the distance under the question.
Then you have this "time" equation
= seconds,
saying that Ahmed and Abdullah spent equal amount of time from the start to the catching (overtaking) moment.
To solve the equation, multiply both sides by 20. You will get
4d = 5*(d-15)
4d = 5d - 75
75 = 5d - 4d
d = 75.
ANSWER. 75 meters from the starting line.
Solved
Using "time" equation is the STANDARD way to solve such problems.
From this solution, learn on how to write, how to use and how to solve a "time" equation.
(1) When both are running, Ahmed makes up 1 meter each second on Abdullah.
(2) The number of meters Ahmed must make up on Abdullah to overtake him is 15.
(3) So the amount of time it will take Ahmed to overtake Abdullah is 15 seconds.
(4) Since Ahmed runs at 5 meters per second, he will overtake Abdullah 15*5=75 meters from the starting line.
