# word problem/ solving and equation

#### needhelpmom

##### New member
A city block is in the shape of a rectangle 800 feet by 600 feet, as shown.
Lee starts at point A running toward point b (a to b is 600 feet).
at a rate of 4.4 feet per second. Lee ran for 2 minutes. Sara who is at point D starts after lee by running toward point A (a to d 800 ft) at a rate of 5.1 feet per second. they continue running around the block until sara catches lee.

How many second does it take dor sara to catch up with lee?

At what point does sara catch up with lee?

:shock:
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#### soroban

##### Elite Member
Hello, needhelpmom!

A city block is in the shape of a rectangle 800 feet by 600 feet, as shown.
Lee starts at point A running toward point B (A to B is 600 feet) at a rate of 4.4 feet/ssecond.
Lee ran for 2 minutes.
Sara who is at point D starts after Lee by running toward point A (A to D = 800 ft) at a rate of 5.1 feet/ssecond.
They continue running around the block until Sara catches Lee.

(a) How many second does it take for Sara to catch up with Lee?

(b) At what point does Sara catch up with Lee?
Lee runs at 4.4 feet/second = 264 feet/minute.
Sara runs at 5.1 feet/second = 306 feet/minute

The difference is speed is: .306 - 264 = 42 ft/sec
. . It is as if Lee is standing still and Sara is running at 42 ft/sec.

Lee has a two-minute headstartL 2 x 264 = 528 feet
Plus Lee started at A (800 feet ahead of Sara): 528 + 800 = 1328 feet.

At the moment that Sara starts running, she has 1328 feet to make up.
. . At 42 ft/min, it will take her: .1328/42 . .31.62 minutes to catch up.
. . [a) 31.6 x 60 .= .1896 seconds.

In 1896 seconds, Sara runs: 1896 x 5.1 = 9889.6 feet (from D).
The distance around the block is: .600 + 800 + 600 + 800 .= .2800 feet.
Since: 9669.6 .= .3(2800) + 1269.6, Sara runs three full laps plus 1269.6 feet past D.

. . (b) Sara catches Lee at: 1269.8 - 800 .= .469.6 feet past point A.

[But someone check my work . . . please!]

#### Denis

##### Senior Member
Agree, soroban.

2800 / 4.4 = 636.3636...
2800 / 5.1 = 549.0196...

Why, oh why, can't teachers keep it simple :evil: