1) Kate pours water into a tank at a constant rate of 320 millilitres per second

Question

1) Kate pours water into a tank at a constant rate of 320 millilitres per second. Water from the first tank spills into a second tank at a constant rate of 30 millilitres per second. If the first tank initially contains 180 millilitres of water, how much will it contain after 42 seconds?

2) Mikael’s bookshelf contains fiction and nonfiction books in the ratio of 5:6. The nonfiction books include only history and science books, in the ratio 5:4. If there are 80 science books, how many books are on the bookshelf altogether?

3) Jesse takes 3 hours to ride 150 km, and Jacob takes 4 hours to ride 240 km. How much longer than Jacob will Jesse take to complete a 280 km journey?

4) Kate pours water into a tank at a constant rate of 250 millilitres per second. Water from the first tank spills into a second tank at a constant rate of 30 millilitres per second. If the first tank initially holds 400 millilitres of water, how long will it take for it to hold 7 L of water?

Explanation / Answer

(1) water poured @ 320 ml/sec but spills in second tank @ 30 ml/sec , hence increasing @ (320 - 30) ml / sec

= 290 ml / sec

hence in 42 sec total water in first tank will be (290 x 42) milliletre = 12180 ml but it is containg already 180 ml

HENCE YOTAL WATER = 12180ML + 180 ML = 12360 MILLILETRE

(2) LET IN NOTIFICATION BOOK, 5 X BOOKS ARE ON HISTORY THEN BOOKS ON SCIENCE WILL BE 4 X

AS RATIO OF HISTORY AND SCIENCE BOOK 5 : 4. NOW GIVEN SCIENCE BOOKS = 80

HENCE 4X = 80 => X = 20 , I.E. HISTORY BOOKS = 5X = 5 (20) = 100 AS X=20

HENCE TOTAL NOTIFICATION BOOKS = 80 + 100 = 180

NOW RATIO OF FICTION AND NOTIFICATION BOOK 5 : 6, LET FICTION BOOKS ARE 5Y THEN NOTIFICATION BOOKS WILL BE 6 Y. NOW 6Y = 180 => Y = 30 HENCE FICTION BOOKS WILL BE

5Y = 5 X 30 = 150 , HENCE TOTAL BOOKS = 150 + 180 =  330

(3) AVERAGE SPEED OF JESSE = 150 KM / 3 = 50 KM/HOUR AND JACOB `S = 240 KM / 4 = 60 KM/HOUR NOW TIME TAKEN BY JESSE TO COVER 280 KM = 280 / 50 = 28/5 HOURS AND JACOB WILL TAKE TO COVER 280 KM = 280 / 60 = 28 /6 HOUR , HENCE REQUIRED LONGER TIME TAKEN BY JESSE WILL BE ( 28 /5 - 28 /6 ) = 28 X 1/ 30 HOUR = 0.93333..... HOUR = 56 SECONDS

(4) RATE OF INCREASE OF WATER IN TANK = ( 250 - 30 ) ML / SEC = 220 ML / SEC

NOW 7 LITRES WATER REQUIRED IN TANK = 7000 ML, BUT TANK IS ALREADY CONTAINING 400 ML WATER , HENCE ADDITIONAL WATER REQUIRED =(7000 - 400) ML = 6600 ML

TIME REQUIRED TO FILL 6600 ML =( 6600 / 220 ) = 30 SEC AS RATE OF FILLING 220 ML / SEC

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