SOLUTION: max leaves kansas city and drive east at a speed of 80km/h. one hour late, olivia leaves kansas city traveling in the same direction as max but at 96 km/h. assuming neither driver

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Question 1057376: max leaves kansas city and drive east at a speed of 80km/h. one hour late, olivia leaves kansas city traveling in the same direction as max but at 96 km/h. assuming neither driver stops for a break, how far from kansas city will they be when olivia catches up with max?
Found 2 solutions by ikleyn, ankor@dixie-net.com:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
max leaves kansas city and drive east at a speed of 80km/h. one hour late, olivia leaves kansas city traveling in
the same direction as max but at 96 km/h. assuming neither driver stops for a break, how far from kansas city will
they be when olivia catches up with max?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

Solution 1 

80%2F%2896-80%29 = 80%2F16 = 5 hours.     (*)

In 5 hours after Olivia's start she will catch up Max.

Olivia will travel 5*96 = 480 km.

Answer.  Olivia will catch up Max at 480 km from Kansas city.

Explanations.  In the formula (*) the numerator "80" is the distance between them when Olivia started her move.

               The denominator 96-80 = 16 km/h is their relative speed.

               The distance between them is decreased 16 km per hour, each hour.

               This "16" is the rate decreasing the distance between the two.

Solution 2 

Let "t" be the time (in hours) after Olivia's start moment till the moment she will catches up Max. 

Then the distance she will cover is 96*t.

Max will spent (t+1) hours and will cover the distance 80*(t+1).

These two distances are the same, so you get an equation 

80*(t+1) = 96*t.

Simplify and solve for t:

80t + 80 = 96t,

80 = 96t - 80t,

16t = 80,

t = 80%2F16   (Do you recognize the formula (*) ?)

t = 5.

Thus Olivia will catch up Max in 5 hours and will cover the distance 5*96 = 480 kilometers.

The same answer.

See the introductory lesson on Travel and Distance problems
    - Travel and Distance problems
in this site.


Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
max leaves Kansas city and drive east at a speed of 80km/h.
one hour later, Olivia leaves Kansas city traveling in the same direction as Max but at 96 km/h. assuming neither driver stops for a break, how far from Kansas city will they be when Olivia catches up with Max?
:
Let t = the travel time of Olivia
then
(t+1) = the travel time of Max
:
When this happens, they will have traveled the same distance
Write a dist equation; dist = speed * time
96t = 80(t+1)
96t = 80t + 80
96t - 80t = 80
16t = 80
t = 80/16
t = 5 hrs
:
Find the distance from K.C
5 * 96 = 480 km
:
Check the distance
80(5 + 1) = 480 km
5 * 96 = 480 km