confusing questions distance/time and work

[sefi]

Faucet A lets water flow into a 5 gallon tub at a rate of 1.5 gallons per minute. Faucet B lets water flow into the same tub at rate of 1 gallon per minute. Faucet A runs alone for 100 seconds, then the two of them together finish filling up the tub. HOw long does the whole operation take?
A 120 seconds
B 150 seconds
C 160 seconds
D 180 seconds
E 190 seconds

Ans C

A man walks down the road for half an hour at an average speed of 3 miles per hour. He waits 10 minutes for a bus, which brings him back to his starting point of 3:15. If the man began his walk at 2:25 the same afternoon, what was the average speed of the bus?

A 1.5mph
B3mph
C4.5mph
D6mph
E9mph

Ans E

[tarkumar]

Faucet A lets water flow into a 5 gallon tub at a rate of 1.5 gallons per minute. Faucet B lets water flow into the same tub at rate of 1 gallon per minute. Faucet A runs alone for 100 seconds, then the two of them together finish filling up the tub. HOw long does the whole operation take?
A 120 seconds
B 150 seconds
C 160 seconds
D 180 seconds
E 190 seconds

Ans C

In 100 sec, water inflow = 1.5 *100/60 = 2.5 gallons
remaining capacity = 5-2.5 = 2.5 gallons
Speed of water inflow when both faucets operates = 2.5 gallons/minute
time take to fill 2.5 gallons = 1 min = 60 sec
total time = 100 + 60

A man walks down the road for half an hour at an average speed of 3 miles per hour. He waits 10 minutes for a bus, which brings him back to his starting point of 3:15. If the man began his walk at 2:25 the same afternoon, what was the average speed of the bus?

A 1.5mph
B3mph
C4.5mph
D6mph
E9mph

Ans E

Total distance travelled by man on foot = half an hour * avg speed
= 0.5 * 3 = 1.5 miles
Time taken by bus = 3:15 (finishing time) - 2:25(starting time) - 0:30 (walking time) - 0:10 (waiting time) = 10 minutes
avg speed of bus = 1.5 m / 10 minutes = 9mph

Hope this helps

[sefi]

thanks but i still don't get the minutes for the bus. if he starts walking at 2:25 and walks for half an hour, thats 3:55 and then waits for the bus for 10 mins so that makes it 3:05..what are those additional ten minutes for?

[Goldust]

The additional 10 minutes are the time it takes for the bus to come back to the starting point.

[ivsham]

For problem 1: I agree that 2,5 gallons remain after A stops working, but how are you sure that A&B complete the job for exactly 1 minute???

[Goldust]

That's because A adds water at a 1.5 gallons/minute, while B adds water at 1 gallon/minute. Together, they add water at 2.5 gallons/minute. Hence, to fill up 2.5 gallons, together they will take 1 minute.

[ivsham]

I see - we asume the velocity of A&B to be the same as A and B separately. Thanks.