Bunuel wrote:
Jake rides his bike for the first 2/3 of the distance from home to school, traveling at 10 miles per hour. He then walks the remaining 1/3 of the distance at 3 miles per hour. If his total trip takes 40 minutes, how many miles is it from Jake's home to his school?
A. \(\frac{5}{4}\)
B. \(\frac{15}{4}\)
C. 5
D. 6
E. 10
Formula used: Average speed = \(\frac{(p+q)*(ab)}{(qa + pb)}\)
where the ratio of the distances traveled is p:q
speeds at which the respective distances are traveled are a and b
Jake rides his bike for the first \(\frac{2}{3}\)rd of the distance and the remaining
\(\frac{1}{3}\)rd of the distance on foot, making the ratio of the distances 2:1(p:q)
Jake travels by bike at speed(a)=10mph and travels by foot at speed(b)=3mph
Substituting values of a,b,p, and q, we get the value for the average speed, as follows
Average speed = \(\frac{(2+1)*(10*3)}{(10 + 6)} = \frac{3*30}{16} = \frac{45}{8}\)
Therefore, the distance traveled by Jake is \(\frac{40}{60}*\frac{45}{8}\) = \(\frac{15}{4}\)
(Option B)
_________________
You've got what it takes, but it will take everything you've got