Problema Solution
Ralph and Josh had a bike race. Since Ralph can ride his bike 400 yards in 1 minute and Josh can ride his bike 350 yards in 1 minute, Ralph gave Josh a 100-yard head start. Ralph crossed the finish line 25 yards ahead of Josh. How many yards did Ralph ride in the race with Josh?
Answer provided by our tutors
let
r = 400 yards per min is the speed of Ralph
j = 350 yards per min is the speed of Josh
t = the time of the ride
d = the distance that Ralph passed
d - 125 = the distance that Josh passed
since speed = distance/time we have
r*t = d
400t = d
j*t = d - 125
350t = d - 125
by solving the system of equations
400t = d
350t = d - 125
we find
d = 1000 yards
t = 2.5 min
click here to see the step by step solution of the system of equations
1000 - 125 = 875 yards
Ralph and Josh rode the bicycle at the same time for 875 yards.