If I run my first 60 km lap at a rate 25 faster than my usua

If I run my first 60 km lap at a rate 25% faster than my usual 12 km/hr, and my second 60 km lap at a rate ___% slower than 12 km/hr, then my overall average speed will be my usual speed
A) 50/3 B) 20 C) 25 D) 250/3

Solution

Usual speed is 12 km/hr
25% faster = 12 + .25*12 = 12*(1+.25) = 12*(1.25) = 15 km/hr
25% slower = 12 - x*12 = 12*(1-x) km/hr

first 60 km lap is done at 15 km/hr
second 60 km lap is done at 12*(1-x) km/hr

overall average is 12km /hr

15 * 60 + 12*(1-x) * 60 = 120 * 12

900 + (12-12x) * 60 = 1440

900 + 720 - 720*x = 1440

add 720*x to both sides of the equation and subtract 1440 from both sides to get:

900 + 720 - 1440 = 720*x

combine like terms to get:

1620 - 1440 = 720*x

combine further to get:

180 = 720*x

divide both sides of the equation by 720 to get:

x = .25

substitute in the original equation to get:

15 * 60 + 12*(1-x) * 60 = 120 * 12 becomes:

15*60 + 12*(1-.25)*60 = 120*12 which becomes:

900 + 12*.75*60 = 1440 which becomes

900 + 540 = 1440 which becomes:

1440 = 1440 which confirms the answer is good.

answer is:

x = .25 * 100% = 25%