500 PS section2 #12

The difference in time (1 hr) can be represented by following equation

450/S - 450/(S+5) = 1

Solving for S, we get 45, -50. Hence C

It might be easier to substitute values from the answer to arrive at
the answer quickly. Choose the middle answer for starters.
We have 450/45 - 450/50 = 1. Which is what we are looking for !

Thanks Jay- it's very clear and good idea to try from C).

The total distance covered during the bus trip is 450 miles.
and, average speed, S, =Total distance covered/ total time taken
S=450/ total time taken
total time taken= 450/S .hour

from the question, the time taken could have been reduced by 1 hour if the average speed S have been increased by 5miles/hr
i.e if Avg. speed (S+5) miles/hr
$$then\ time=\left(\frac{450}{S}d-\frac{1}{ }\right)\ hr$$
$$Therefore,S+5=\frac{total\ dis\tan ce}{\frac{450}{S}-1}$$
Since distance is still the same,
$$Therefore,S+5=\frac{450}{\frac{450}{S}-1}$$
$$\left(S+5\right)\left(\frac{450}{S}-1\right)=450$$
By expanding the expression on the left, we have,
$$450-S+\frac{2250}{S}-5=450$$
$$S+5-\frac{2250}{S}=0$$
$$S^2+5S-2250=0$$
solving this quadratically, we obtain
(S+50)(S-45)=0
S=-50 or S=45 miles/hr

since average speed cannot be negative, we will discard the negative value obtained.
Average speed, S= 45 miles/hr