Ratio and proportion

nidhis.1408 wrote:It takes the average dryer 80 minutes to dry one full load of Bob's laundry. Bob has one average dryer, and also decides to try one "Super Jumbo-Iron Dryer-Matic", which is faster than the average dryer by a ratio of 5 : 4. Bob has three loads of laundry, and both machines are so precise that he can set them to the minute. How many minutes does it take for him to dry his three loads? (Assume that no time passes between loads and that he can use both machines concurrently. Assume also that he never runs a machine with less than a full load. Finally, assume that Bob does not partially dry a load in one machine and then switch it to the other.)


Kindly explain the solution . Its a problem from Manhattan word translation guide.

Slower machine takes = 80 minutes.
Faster machine is 5:4 times faster. Therefore it does loads in = 4/5*80 = 4*16 = 64 minutes.

Now if Bob puts three loads, for the minimum time required, for no switching is when he starts with two loads in two machines, one in slower and one in faster one. Slower one is done with the load in 64 minutes, the faster one is still drying.

Now he puts second load in the faster one, and starts it again. So the second load is going to take 64 more minutes. In the meantime, the slower machine is done after total of 80 minutes. The faster one dries the other two loads in 64+64 = 128 minutes.
Hence overall time to dry = 128 minutes.

By the way the question should read "What is the minimum time required for Bob to dry the loads? "

nidhis.1408 wrote:It takes the average dryer 80 minutes to dry one full load of Bob's laundry. Bob has one average dryer, and also decides to try one "Super Jumbo-Iron Dryer-Matic", which is faster than the average dryer by a ratio of 5 : 4. Bob has three loads of laundry, and both machines are so precise that he can set them to the minute. How many minutes does it take for him to dry his three loads? (Assume that no time passes between loads and that he can use both machines concurrently. Assume also that he never runs a machine with less than a full load. Finally, assume that Bob does not partially dry a load in one machine and then switch it to the other.)


Kindly explain the solution . Its a problem from Manhattan word translation guide.

Since the rate ratio = 5:4, let the rate of the fast machine = 5 units per minute and the rate of the slow machine = 4 units per minute.
Since the slow machine completes one load in 80 minutes, one load = r*t = 4*80 = 320 units.
Time for the fast machine to complete 320 units = w/r = 320/5 = 64 minutes.
Thus, the fast machine can complete 2 loads in 128 minutes -- more than enough time for the slow machine to complete 1 load.
Thus, the 3 loads will be completed in 128 minutes.