jabhatta@umail.iu.edu wrote:
VeritasKarishma wrote:
ichha148 wrote:
Tanks X and Y contain 500 and 200 gallons of water respectively. If water is being pumped out of tank X at a rate of K gallons per minute and water is being added to tank Y at a rate of M gallons per minute, how many hours will elapse before the two tanks contain equal amounts of water?
A. \(\frac{5}{M + K}\text{ hours}\)
B. \(6(M + K)\text{ hours}\)
C. \(\frac{300}{M + K}\text{ hours}\)
D. \(\frac{300}{M - K}\text{ hours}\)
E. \(\frac{60}{M - K}\text{ hours}\)
m22 q17
This is a relative speed question.
Distance to be covered together = 300 gallons (= 500 gallons - 200 gallons)
Relative speed (rate of work) = (K+M) gallons per minute OR 60*(K+M) gallons per hour (The rates get added because they are working in opposite directions)
Time taken = 300/60(K+M) hours = 5/(K+M) hours
Hi
karishmaIn relative speed questions -- why do we add the rates [M+K] that are working in opposite directions ? Could you perhaps explain why we are adding in this case and not subtracting
Also, you mentioned above that relative speeds are similar to relative rates...
But i thought relative rates are such that
-- if two people are working together on the project [rates in the same direction] - we can add the rates for a combined rates [ R1 + R2]
-- if one person is constructing and the other person is de-constructing a project [rates in the opposite direction] - the combined rate is obviously R1 - R2
Thank you !
Say A and B are standing at two ends of a track of 300 m
A ->----------------- (300 m)---------------------<- B
Now they have to meet so A will start walking towards B (due east direction) and B will start walking towards A (due west direction). They are walking in opposite directions towards each other.
--------------AB---------------------------------
Say they meet here. Together they have covered 300 m. So if A's speed were 100 m/hr and B's speed were 200 m/hr, in 1 hr they would together cover 300 m.
Now say they start walking in opposite directions again away from each other. A starts walking due west and B starts walking due east.
-----------<-A--B->--------------------------------
In one hr, they will again cover 300 m together.
A ------------------ (300 m)---------------------- B
So whenever two objects are moving in opposite directions, their speeds get added.