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        riddles >> medium >> Bridge and river
        
(Message started by: Altamira_64 on Jul 24^th, 2013, 10:47am)

Title: Bridge and river
Post by Altamira_64 on Jul 24^th, 2013, 10:47am

Anna left town A at 10:18 am. She walked at a constant speed and arrived at town B at 1:30 pm. On the same day, Bob left town B at 9 am. Bob walked the same route in the opposite direction at a constant speed and arrived at town A at 11:40 am. The road crosses a wide river. By coincidence, both arrived at the bridge on opposite sides of the river at the same instant. Anna left the bridge 1 minute later than Bob. At what time did they arrive at the bridge?

Title: Re: Bridge and river
Post by jollytall on Jul 24^th, 2013, 9:24pm

11:00

[hideb]A walked 192 minutes. Let be her speed 1 Ann/minute, where Ann is a distance unit.
The total distance is 192Ann.
B walked 160 minutes, i.e. his speed is 1.2Ann/minute.
They reach the bridge X minutes after 9:00.
A walked X-78 minutes, i.e. X-78 Ann.
B walked X minutes, i.e. 1.2*X Ann.

B crosses the bridge in Z minutes, i.e. 1,2*Z Ann long.
A crosses the bridge in Z+1 minutes, i.e. Z+1 Ann long.
Z=5. The bridge is 6Ann long.

After X minutes we have X-78 + 6 + 1.2*X = 192
2.2*X = 264
X=120.
They reach the bridge at 11:00[/hideb]