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

Click here to see ALL problems on Miscellaneous Word Problems

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