two towns are 80 km apart kasia wants to drive from one tow

two towns are 80 km apart . kasia wants to drive from one town to the other in exactly one hour. for the first 30 minutes she drives at a rate of 60 km/h. the constant rate , in km/h, at which she must drive for the next 30 minutes to accomplish her goal is
(a) 20 (b) 40 (c) 50 (d) 80 (e) 100

Solution

t = 1
d = 80 km

first part of the trip, rate * time was .5 * 60
second part of the trip, rate * time will be .5 * x

add the parts together to get the total trip.

.5 * 60 + .5 * x = 80

30 + .5x = 80

subtract 30 from both sides to get:

.5x = 50

divide both sides by .5 to get:

x = 100

confirm by plugging into the original equation to get:

.5 * 60 + .5 * 100 = 80

simlify to get:

30 + 50 = 80 confirming the answer for x is good.