I T
W _ L L
T _ K _
4
H _ _ R S
4 3
M _ N S
1 6 . 7 2
S _ C _ N D S
T _
F _ L L
T H _
P _ _ L .
I N
_ N _
H _ _ R :
1 S T
T _ P
F _ L L S
1 / 4 8
_ F
T H _
P _ _ L
2 N D
T _ P
F _ L L S
1 / 7 2
_ F
T H _
P _ _ L
3 R D
T _ P
F _ L L S
1 / 9 6
_ F
T H _
P _ _ L
4 T H
T _ P
F _ L L S
1 / 6
_ F
T H _
P _ _ L
T H _ S
_ D D S
_ P
T _
6 1 / 2 8 8
( 1 / 4 8
+
1 / 7 2
+
1 / 9 6
+
1 / 6 )
F _ R
1
H _ _ R .
T _
F _ L L
T H _
P _ _ L ,
_ T
W _ L L
T _ K _
2 8 8 / 6 1
H _ _ R S Clue
IT WILL TAKE 4 HOURS 43 MINS 16.72 SECONDS TO FILL THE POOL. IN ONE HOUR: 1ST TAP FILLS 1/48 OF THE POOL 2ND TAP FILLS 1/72 OF THE POOL 3RD TAP FILLS 1/96 OF THE POOL 4TH TAP FILLS 1/6 OF THE POOL THIS ADDS UP TO 61/288 (1/48 + 1/72 + 1/96 + 1/6) FOR 1 HOUR. TO FILL THE POOL, IT WILL TAKE 288/61 HOURS FOR THE TRAIN TO PASS COMPLETELY THROUGH THE TUNNEL, IT MUST TRAVEL 2 MILES. AFTER 1 MILE TRAVEL, THE TRAIN WOULD BE COMPLETELY IN THE TUNNEL, AND AFTER ANOTHER MILE IT WOULD BE COMPLETELY OUT AND SINCE THE TRAIN IS TRAVELING AT 1 MILE A MINUTE, IT WILL TAKE 2 MINUTES TO PASS THROUGH THE TUNNEL 45 MINUTES. METHOD 1 LET US TALK ABOUT 24 HOURS AS IT WILL SIMPLIFY THE PROBLEM. IN 24 HOURS: THE COLD TAP WILL BE ABLE TO FILL THE BATHTUB 80 TIMES. THE HOT TAP WILL BE ABLE TO FILL THE BATHTUB 96 TIMES. THE DRAIN WILL BE ABLE TO DRAIN THE BATHTUB 144 TIMES. THUS IN 24 HOURS, THE BATHTUB WILL BE FILLED 80 + 96 - 144 = 32 TIMES (IF BOTH TAPS ARE TURNED ON WITH THE PLUG LEFT OUT) THUS IT WILL TAKE 45 MINUTES TO FILL THE TUB ONCE. METHOD 2 THE BATHTUB FILLING RATE IS: THE COLD TAP WILL FILL THE BATHTUB AT 1/18 TUB/MINUTE THE HOT TAP WILL FILL THE BATHTUB AT 1/15 TUB/MINUTE THE DRAIN WILL DRAIN THE BATHTUB AT 1/10 TUB/MINUTE THE NETT BATHTUB FILL RATE IS: 1/18 + 1/15 - 1/10 = 1/45 TUB/MINUTE THE WATER WILL FILL 1/45 OF THE TUB IN 1 MINUTE, SO THE TUB WILL BE FULL IN 45 MINUTES IT WILL TAKE 5 DAYS FOR 100 PEOPLE TO BUILD 100 HOUSES. 1 PERSON CAN BUILD 1 HOUSE IN 5 DAYS. SO, 100 PEOPLE CAN BUILD 100 HOUSES IN 5 DAYS