# math

in his spare time, kim likes to go cycling. he cycles partly on paved surfaces and partly off-road, through hilly and wooded areas. he cycles at 25km/hon paved surfacesand at 10 km/h off-road. one day, he cycled 41km in 2h. how far did he cycle off road?

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1. Two equations, two unknowns.
Let x be the number of offroad km travelled, and y be the number of km on roads.

x + y = 41 (kilometers)

10/x + 25/y = 2 (hours)

Solve for x and y.

10 + 25x/(41-x) = 2x

You end up with a quadratic equation. Take the positive root for x.

If you are not learning algebra yet, you can use a "trial and error" method.

If x = 25 and y = 16, the time spend off roads is 2.5 hours and off raods is 1,6 hours and the totl is 4.1 which is much more than 2 hours.

If x = 5 and y = 36 hours, the time spent off roads is 0.5 hours and the time spent on roads is 1.44 hours, and the totasl is 1.94 hours. You need a bit more time off roads to require 2 hours.

6/10 + 35/25 = 2.0

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2. Cycled X-hrs on paved surfaces.

=
Eq1: X + Y = 2 hrs.

Eq2: 25X + 10Y = 41km.
Multiply Eq1 by -10 and add Eq1 and Eq2.

-10X -10Y = -20,
25X + 10Y = 41,
Sum: 15X + 0 = 21,
X = 1.4 hrs on paved roads.

Substitute 1.4 for X in Eq1:
1.4 + y = 2,

d = Vt = 10km/h * 0.6h = 6km off-road.

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3. thanks :)

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