SOLUTION: The Smith family and the Jones family are next-door neighbors and are driving to Las Vegas in separate cars for vacation. They are traveling on the same road in the same direction.

Question 443214: The Smith family and the Jones family are next-door neighbors and are driving to Las Vegas in separate cars for vacation. They are traveling on the same road in the same direction. The Smith family leaves at 8:00am and drives 70mph. Because of a luggage malfunction, the Jones family leaves at 10:00 am and drives 20% faster than the Smith family in an attempt to catch them.
A. How long will it take the Jones family to catch the Smith family? 12 hrs
B.At what time of day will this occur? 8 pm
C. How far from the starting point will they be when the Jones family catches the Smith Family? 840 miles

I cannot figure out how to write the equation I figured out the answers on a bar graph
Found 3 solutions by rwm, ankor@dixie-net.com, stanbon:
Answer by rwm(914)   (Show Source): You can put this solution on YOUR website!
Where did they start from? LA isn't that far away!
r*t=d
70*(t+2)=d
1.2*70*t=d
the distance will be the same so we set them equal
70*(t+2)=1.2*70*t
divide by 70
t+2=1.2t
subtract t
2=.2t
divide by 2
1=.1t
multiply by 10
10=t
check
70*12=1.2*70*10
70*12=12*70
ok
it took ten hours for the jones to catch the smiths. The smiths traveled 12 hours but the jones only 10
everything else is correct
the jones travelled at 84 mph
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
The Smith family and the Jones family are next-door neighbors and are driving to Las Vegas in separate cars for vacation. They are traveling on the same road in
the same direction. The Smith family leaves at 8:00am and drives 70mph.
Because of a luggage malfunction, the Jones family leaves at 10:00 am and drives
20% faster than the Smith family in an attempt to catch them.
;
A. How long will it take the Jones family to catch the Smith family?
Let t = travel time of Jones
then
(t+2) = travel time of Smith
:
Find Jones' speed: 1.2(70) = 84 mph
:
When J catches S, they will have traveled the same distance
write a distance equation Dist = speed * time
:
84t = 70(t+2)
84t = 70t + 140
84t - 70t = 140
14t = 140
t =
t = 10 hrs is Jones travel time
:
B.At what time of day will this occur?
10 Am + 10 hrs = 8 Pm
:
C. How far from the starting point will they be when the Jones family catches the Smith Family?
84 * 10 = 840 mi
:
Confirm this by finding the dist of the Smiths
70 * 12 = 840 mi
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
They are traveling on the same road in the same direction.
The Smith family leaves at 8:00am and drives 70mph.
---
Smith DATA:
rate = 70 mph ; time = t hrs ; distance = rt = 70t miles
---------------------------
Because of a luggage malfunction, the Jones family leaves at 10:00 am and drives 20% faster than the Smith family in an attempt to catch them.
---
Jones DATA:
rate = 1.2(70) = 84 mph ; time = t-2 hrs ; distance = 84(t-2) = 84t-168 miles
-----------------

A. How long will it take the Jones family to catch the Smith family?
Equation:
84t-168 = 70t
14t = 168
t = 12 hrs.
-------------------------------
B.At what time of day will this occur? 8 pm
-------------------------------
C. How far from the starting point will they be when the Jones family catches the Smith Family? 840 miles
Distance = rate*time = 70*12 = 840 miles
==========================================
Cheers,
Stan H.

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