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Amit B.
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Basic Math
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Question:

If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?

Amit B.
Answer:

Here, we see that going with different speeds a man reaches his destination at different times, but implicit in problem is that the distance travelled by him (d) is a constant. So let's assume his time taken for two instances be t1 and t2 and we know that t2 is 2 hours lesser than t1. As we know, Distance (d) = Speed (s) * Time (t), therefore in first scenario d = 10 * t1 and in second d = 15 * t2 As d is a constant in both the equations, equating both we get 10t1 = 15t2 Or t1/t2 = 15/10 = 3/2 Or t1 = 3/2 t2 And we know t1 - t2 = 2 hours Therefore, replacing t1 as 3/2t2 in the above equation we get 3/2 t2 - t2 = 2 1/2 t2 = 2 t2 = 2*2 = 4 and t1 = 3/2t2 = 3/2 (4) = 6 thus, Distance (d) = 10 * t1 = 10 * 6 = 60 kms Now when he takes t2, i.e. 4 hours to reach his destination, he arrives at 11 a.m. and when he takes t1 = 6 hours, he arrives at 1 p.m. To arrive at 12 noon, he must take 5 hours of time Thus we have the person traveling 60 kms in 5 hours, his speed will be s = 60/5 = 12 km/h So he needs to travel at 12 km/h to reach at noon.

Psychology
TutorMe
Question:

Forgetting is natural, while extinction is experimentally induced. Elaborate

Amit B.
Answer:

Forgetting is loss of information from long term memory because of retention failure or retrieval failure. It is a natural process and may occur due to improper encoding, interference, wrong cues or unconscious factors. Extinction, on the other hand, also involves loss of information or previously learned behavior but unlike forgetting it is experimentally induced via not pairing Conditioned Stimuli with UnConditioned Stimuli (classical conditioning), or not reinforcing behavior(operant conditioning).

Algebra
TutorMe
Question:

Five consecutive positive integers have a sum Z, find the sum of next five consecutive integers in terms of Z.

Amit B.
Answer:

Let's assume the least of the five given integers be x, So the next four consecutive integers would be x+1, x+2, x+3 and x+4 Their sum, given as Z, would be x + (x+1) + (x+2) + (x+3) + (x+4) Or Z = 5x + 10 Or x = (Z - 10)/5 Next five consecutive integers would be (x+5), (x+6), (x+7), (x+8), (x+9) and their sum S would be S = (x+5) + (x+6) + (x+7) + (x+8) + (x+9) = 5x + (5+6+7+8+9) = 5x + 35 substituting x in terms of Z obtained above, we get S = 5[(Z-10)/5] +35 = Z - 10 + 35 = Z + 25 Thus, the sum of next five integers in terms of Z would be Z + 25.

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