Answer:
The run is 4.875 miles long, while, the bike is 6.875 miles long.
Step-by-step explanation:
Let d = running distance and d' = biking distance.
Given that d' = d + 2 and v = running speed = 6 mph and v' = biking speed = 10 mph.
Since time, t = distance/speed, running time, t = running distance/running speed = d/6 and biking time, t' = biking distance/biking time = d'/10 = (d + 2)/10.
Since the total time, t" = 90 minutes = 1.5 hours,
t + t' = t"
So, d/6 + (d + 2)/10 = 1.5
multiplying through by the L.C.M, 30, we have
30 × d/6 + 30 ×(d + 2)/10 = 30 × 1.5
5d + 3(d + 2) = 45
expanding the brackets, we have
5d + 3d + 6 = 45
collecting like terms, we have
8d = 45 - 6
8d = 39
d = 39/8
d = 4.875 miles
d' = d + 2 = 4.875 + 2 = 6.875 miles
So, the run is 4.875 miles long, while, the bike is 6.875 miles long.
