Solving problems including direct proportionality

Algebra 1 Tutorial

Solving problems including direct proportionality

Intro

These types of problems seem to be very simple , yet students have a lot of problems solving them due to lengthy solutions given by most of school teachers. In here we’ll solve them the easy, and fast way.
Difficult wording is another issue, so we’ll analyze the problem to find the key numbers that lead to the solution.

Sample Problem

Usain Bolt can run 100m in 9.58 seconds, whereas Asafa Powell can run the same distance in 9.74 seconds. Considering that they keep a constant speed during their runs, how much faster will Bolt cross the line of 800m distance?

Solution

For Bolt,

9.58sec <--> 100m
X sec <--> 800m

We cross multiply: 9.58*800=X*100
Dividing both sides by 100, we get X=9.58*8=76.64 seconds that Bolt needs to run 800m.

For Powell,

9.74sec <--> 100m
Y sec <--> 800m

We cross multiply: 9.74*800=Y*100
Dividing both sides by 100, we get Y=9.74*8=77.6 seconds that Powell needs to run 800m.

Now we find the difference in these times by subtracting the shortest time from the longest time.
77.6-76.64=0.96 seconds.
Therefore, Bolt will cross the line 0.96 seconds faster.



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