Solution:

10 miles

Solution:

48 minutes.

Donald duck's speed = X km/seconds
pool current speed = Y km/seconds

2/(X+Y) = 40
2/(X-Y) = 60

Solving the simultaneous equations gives X = 1/24

Therefore, to cover 2km will take 2/X = 48 seconds

Solution:

3 hours

Explanation :
(1/4 + 1/6 - 1/12) ^ (-1)
= (1/3)^(-1) = 3

Solution:

24miles/hr (not 25miles/hr which might be guessed by many)

D : distance traveled
T1 : time of going to office
T2 : time of returning back
Y : Average Speed

D = 20 * T1
T1 = D/20

D = 30 * T2
T2 = D/30


2D = Y(T2 + T1)
2D = Y(D/20 + D/30)
2D = Y(3D/60 + 2D/60)
2D = Y(5D/60)
Y = 120D/5D

=> Y = 24

Solution:

1. Start both the 7 minute hour glass & 11 minute hour glass.
2. Wait till the 7 minute hour glass times out. Time is 7 minute!
3. Restart the 7 minute hour glass. At this time 11 minute hour glass will have 4 minutes left to time out.
4. As soon as 11 minute glass times out invert the 7 minute hour glass. Total time now is 11 minutes.
5. After inverting 7 minute hour glass, it will now have 4 minutes left for time out.
6. After these 4 minutes times out, the total time is 15 minutes.

Solution:

In one hour,

Soln 1:
the large inlet tube fills 1 / 3 of the tank;
the small inlet tube fills 1 / 6 of the tank;
the outlet tube empties 1 / 9 of the tank; and therefore
all three tubes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank.

Fraction of the tank that will be filled in 0.64 hours =
0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.


Soln 2:
Let V be the total volume of the tank. From equation (1),

Flow Rate (large inlet tube) = V / 3
Flow Rate (small inlet tube) = V / 6
Flow Rate (outlet tube) = V / 9.

Substituting in equation (2),

Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9).

Using the above result in equation (1),

Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ].

Note that V cancels out on simplifying the above expression.

Fraction of the tank that will be filled in 0.64 hours =

0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.

Solution:

Both would be the same distance from City owlna. (since they are at a same point)

Solution:

5:19

Starting with the watch on the left, add 42 minutes to the time shown to give the time on the next watch to the right

Solution:

17 min

The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 minutes. Is that it? No. That would make this question too simple even as a warm up question.

Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.

1 and 2 go cross
2 comes back
7 and 10 go across
1 comes back
1 and 2 go across (done)

Total time = 2 + 2 + 10 + 1 + 2 = 17 minutes

Solution:

2100 miles.

Each vowel equivalent to 500 and each consonant equivalent to -200