Question

If stewart and patrick can finish a science project together in 20 minutes, and Patrick works four times as quickly as Stewart, how long would it take Patrick to complete the project alone?

Answer 1

Answer:

It would take 25 minutes for Patrick to complete the project alone.

Step-by-step explanation:

They did the project in 20 minutes, that is, 100% of the project, so:

$x + y = 1$

In which x is the percentage that Patrick worked and y is the percentage that Stewart worked.

Patrick works four times as quickly as Stewart, so x = 4y.

So

$x + y = 1$

$4y + y = 1$

$5y = 1$

$y = 0.2$

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$x = 4y = 4*0.2 = 0.8$

Patrick did 80% of the project in 20 minutes. We can solve this problem by a simple rule of three, in which the time it would take for him to complete the project alone is 100%. So

20 minutes - 0.8

x minutes - 1

$0.8x = 20$

$x = 25$

It would take 25 minutes for Patrick to complete the project alone.