Roger can run one mile in 24minutes. Jeff can run one mile in 21minutes. If Jeff gives Roger a 11 minute head​ start, how long will it take before Jeff catches up to​ Roger? How far will each have​ run? Not including the head​ start, it will take_____minutes for Jeff to catch up to Roger.

Question
Asked Sep 11, 2019
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Roger can run one mile in 24minutes. Jeff can run one mile in 21
minutes. If Jeff gives Roger a 11 minute head​ start, how long will it take before Jeff catches up to​ Roger? How far will each have​ run?
 
Not including the head​ start, it will take_____minutes for Jeff to catch up to Roger.
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Expert Answer

Step 1

Data of Roger,

Roger runs 1 mile in 24 minutes.

So, Rate by which Roger is running = 1/24 mile/ minute.

Let, Roger runs for x minutes.

So, total distance ran by Roger = rate * time = x/24 mile.

Step 2

Data of Jeff,

Jeff runs 1 mile in 21 minutes.

So, Rate by which Jeff is running = 1/21 mile/ minute.

As Jeff gives Roger a 11minute head start, so Jeff will run for (x-11) minutes.

So, total distance ran by Jeff = rate * time = (x-11)/21 mile.

Step 3

Both Roger and Jeff must cover the same dist...

х — 11
х
24
21
х — 11
0
X
=>
24
21
7х — 8(х — 11)
0
168
x 88 0
88 minutes
X
88
-mile
24
X
mile
24
So, distance ran by Roger
3.67 mile
(х — 11)
mile
77
-mile
21
3.67 mile
And, distance ran by Jeff
21
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Image Transcriptionclose

х — 11 х 24 21 х — 11 0 X => 24 21 7х — 8(х — 11) 0 168 x 88 0 88 minutes X 88 -mile 24 X mile 24 So, distance ran by Roger 3.67 mile (х — 11) mile 77 -mile 21 3.67 mile And, distance ran by Jeff 21

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Algebra