Here's the first one:

4x + 3x + 2x = 36

9x = 36

x = 4

So the secretaries type at 16, 12, and 8 pages per 1/2 hr respectively. The slowest-typing is 8 pages per 1/2 hour, or 16 pages per hour. To type 52 pages it will take her 52/16 hours, or 3.25.

The answer is D.

2nd Que -

Lionel left his house and walked towards Walt's house, 48 miles away. Two hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 4 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt? (A) 12 (B) 16 (C) 20 (D) 24 (E) 28

in 2 hours L has already walked (2 * 4) = 8 miles. so when W starts running the distance between the two is 40 miles.
since direction of L and W is opposite we can their relative speed = 4 + 6 = 10 mph.
so it would take 4 hours to cover distance of 40 miles

In those 4 hours, L would have covered 4 * 4 = 16 miles

so total distance covered by L = 8 + 16 = 24 miles. Ans D.

Hope this helps...

QUe 3-

Andrew and Stephen drive on the highway in the same direction at respective rates of 72 and 80 kmh. If Stephen is 4 km behind Andrew, by how much does he have to increase his speed to catch up with Andrew in 20 minutes? (A) 1 kmh (B) 2 kmh (C) 3 kmh (D) 4 kmh (E) 5 kmh

the relative speed of A and S = 80 - 72 = 8 kmph

so with this relative speed S would take 30 mins to cover the distance of 4 km
however S needs to cover the distance of 4 km in 20 mins that is 1/3 hour.

so since speed = dist / time
speed = 4 / (1/3) = 12 kmph
But the relative speed is 8 kmph so S would need to increase his speed by 12 - 8 = 4 kmph

hope this helps...

Sumgb's answer is the best, and simplifies the question considerably using relative speed. My approach was different, because I wasn't able to see the relative speed, but I believe this is easier to understand.

S needs to catch up to A, and A is already 4km ahead. Not only that, but whatever time you need to gain that 4km, A is going to continue moving ahead

D=RT, and the D is going to be the distance we want S to cover.

4km + distance A would move = Speed of S x T, let T be the time.

4km + 72*T = 80*T.

if you solved for T here, you get the amount of time it takes for S to catch up to A going at their existing speeds as question stated. But we don't want to solve for T. We know T = 20 minutes, so another item must vary, and that is 80 because that is speed of S and we're asked to vary the speed of S.

20 minutes = 1/3 hour

4km + 72/3 = (80+V)*1/3 where V is the difference in velocity S needs. Notice all the 20 minutes are now plugged in as 1/3.

4 + 24 = 80/3 + V/3
28 = 80/3 + V/3
84 = 80 + V
4 = V