Word problems using inequalities 2.?

Question

Jose wants to swim part of the way and run part of the way to a friends house. The distance from Jose's house to his friends house along the straight shore of a lake is 2 km. If he runs 18hm/h and swims at 2km/h, what is the greatest distance he can swim and still arrive in less than 20 minutes.

Answer 1

x + y = 2 km

18 km/h = .3 km/min = 10/3 min/km
2 km/h = 1/30 km/min = 30 min/lm

So: 10/3 x + 30 y < 20 min

Define y in terms of x: y = 2-x
Substitute y: 10/3 x + 30 * (2-x) < 20 min
10/3 x + 60 - 30 x < 20 min
-80/3 x + 60 < 20 min
-80/3 x < -40
x > 3/2 km (Remember - the inequality switches if you multiply by a negative number)
y < 1/2 km - Jose must swim less than 1/2 km to be able to get there in less than 20 minutes.

check:
1/2 km / 2 km/h = 1/4 hr = 15 min
3/2 km / 18 km/h = 1/12 hr = 5 min.