SOLUTION: Max was crossing a narrow bridge. When he was 3/5 of the way across, he saw a truck approachen the bridge 600 yards away from him and heading right toward him. He turned and ran ba

Question 236649: Max was crossing a narrow bridge. When he was 3/5 of the way across, he saw a truck approachen the bridge 600 yards away from him and heading right toward him. He turned and ran back. The truck continued at the same speed and missed him by a hair. If Max had tried to cross the bridge, the truck also would have just missed him. How long was the bridge?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Max was crossing a narrow bridge.
When he was 3/5 of the way across, he saw a truck approachen the bridge 600 yards away from him and heading right toward him.
He turned and ran back.
The truck continued at the same speed and missed him by a hair.
If Max had tried to cross the bridge, the truck also would have just missed him.
How long was the bridge?
:
|-------3x-------Max-----2x-----|_____(600-2x)__________Truck
:
5x = length of the bridge
Truck is 600 ft from Max, which is (600-2x) from bridge
:
Use the ratio of the truck dist to Max dist, is the same in both situations
Situation 1
Max covers 3x while truck covers 600+3x
Situation 2
Max covers 2x while truck covers 600-2x
:
A ratio equation:
+
Cross multiply
2x(600+3x) = 3x(600-2x)
1200x + 6x^2 = 1800x - 6x^2
6x^2 + 6x^2 + 1200x - 1800x = 0
12x^2 - 600x = 0
12x(x - 50) = 0
x = 50, the bridge is 5x: 5 * 50 = 250 yds
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