A car traveled 75% of the way from town A to town B by traveling at T hours at an average speed of V mph. The car travels at an average speed of S mph for the remaining part of the trip. Which of the following expressions represents the average speed for the entire trip?
$$A.\ 0.75V+0.25S$$
$$B.\ 0.75T+0.25S$$
$$C.\ \frac{VT}{3S}$$
$$D.\ \frac{4VT}{\frac{\left(T+S\right)}{3}}$$
$$E.\ \frac{4VS}{3S+V}$$
The OA is E.
Can I say that total distance is 100 miles, then
75% of the total distance will be, 75 miles at an average speed of V mph, that's mean that the time for this 75% will be 75/V.
25% of the total distance will be, 25 miles at an average speed of S mph, that's mean that the time for this 25% will be 25/S.
Hence, the total average speed will be,
$$A_s=\frac{100}{\frac{75}{V}+\frac{25}{S}}=\frac{100}{\frac{75S+25V}{VS}}=\frac{100VS}{25\left(3S+V\right)}=\frac{4VS}{3S+V}$$
Experts, any suggestion about this PS question? Thanks in advance.
$$A.\ 0.75V+0.25S$$
$$B.\ 0.75T+0.25S$$
$$C.\ \frac{VT}{3S}$$
$$D.\ \frac{4VT}{\frac{\left(T+S\right)}{3}}$$
$$E.\ \frac{4VS}{3S+V}$$
The OA is E.
Can I say that total distance is 100 miles, then
75% of the total distance will be, 75 miles at an average speed of V mph, that's mean that the time for this 75% will be 75/V.
25% of the total distance will be, 25 miles at an average speed of S mph, that's mean that the time for this 25% will be 25/S.
Hence, the total average speed will be,
$$A_s=\frac{100}{\frac{75}{V}+\frac{25}{S}}=\frac{100}{\frac{75S+25V}{VS}}=\frac{100VS}{25\left(3S+V\right)}=\frac{4VS}{3S+V}$$
Experts, any suggestion about this PS question? Thanks in advance.
