Problem Solving

Source: Economist GMAT

Tammy climbed a mountain in two days. She spent a total of 14 hours climbing the mountain. On the second day, she walked at an average speed that was half a kilometer per hour faster, but 2 hours less than what she walked on the first day. If the total distance she climbed during the two days is 52 kilometers, how many kilometers per hour did Tammy walk on the second day?

A. 3
B. 3.5
C. 4
D. 4.5
E. 6

The OA is C

Time on day 1 = x
Time on day 2 = x - 2
Total time = Day 1 + Day 2
14 = x + x -2
14 = 2x - 2
16 = 2x
x = 8
$$Total\ speed\ =\ \frac{Total\ dis\tan ce}{Total\ time}$$
$$Day\ 1\ =\ speed\ \cdot\ 8=Dis\tan ce$$
$$Day\ 2=\ \left(Speed+0.5\right)\cdot6=52-d$$
$$52=s\cdot8+\left(s+0.5\right)\left(8-2\right)$$
$$52=8s+8s-2s+4-1$$
$$52=14s+3$$
$$\frac{49}{14}=\frac{14s}{14}$$
$$s=3.5$$
But her speed was 0.5 km/hr faster on day 2
Day 2 speed $$3.5+0.5=4.0\ \frac{km}{hr}$$
$$Answer\ is\ Option\ C$$