Question 284699: Chuck Travels 80 km in the same time that Mary travels 180 km. Mary travels 50 km per hour faster than Chuck. Find the rate of each person.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The basic distance equation is useful: D = RT, where D=Distance, R=Rate of speed & T = Time.
DC = Chuck's distance = 80 km
DM = Mary's distance = 180 km
T = Chuck's time = Mary's time
RC = Chuck's rate of speed
RM = Mary's rate of speed
RM = RC + 50 kph :: Mary is going 50 km/hr faster.
.
Since they travel for the same time, but you do not know the time, you need to eliminate it.
.
We know the distance travelled at speed = RC.
.
80 = RC*T
.
So we can define T = 80/RC
.
And we know the distance travelled at speed = RM.
.
180 = RM*T
.
So we can define T = 180/RM
.
Using the transitive property to eliminate T.
.
80/RC = 180/RM
.
Substitute RM = RC+50.
.
80/RC = 180/(RC+50)
.
Cross multiply to eliminate denominators.
.
80*(RC+50) = 180*RC
.
80*RC + 4000 = 180*RC
.
4000 = 180*RC - 100*RC
.
4000 = 100*RC
.
RC = 4000/100 = 40 km/hr
.
Now we can substitute that value to get RM.
.
RM = RC+50
.
RM = 40 + 50 = 90 km/hr
.
Checking to see if these are the answer.
.
80 = 40*T
T = 80/40 = 2 hr
.
180 = 90*T
T = 180/90 = 2 hr
.
Correct!
.
Answer:
Chuck's speed is 40 km/hr.
Mary's speed is 90 km/hr.
.
Done.
|
|
|
