A runs 25% faster than B and is able to give him a start of 7 meters to end a race in dead heat. What is the length of the race?
Notice that the distance that A runs 7 meters more than B, so:
d_a = d_b + 7
Since distance = rate * time, re-write this:
(r_a)(t_a) = (r_b)(t_b) + 7
Since A runs 25% faster than B, re-write as follows:
(1.25*r_b)(t_a) = (r_b)(t_b) + 7
Now, the other catch is that they finish in dead heat, so their times are equal, so change t_a to t_b
(1.25*r_b)(t_b) - (r_b)(t_b) = 7
(1.25*r_b)(t_b) - (r_b)(t_b) = 7
(1.25 - 1)(r_b*t_b) = 7
r_b*t_b = 7 / .25
d_b = 28
Since B goes 28 meters, that means A goes 35 meters, so the length of the race is 35 meters.
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