A car leaves a city traveling at 5O MPH an hour later a car leaves the the city travling at 70 in chase of car

Question

I've been working on this for 2 days HELP!!!!

A car leaves a city traveling at 5O MPH. A hour later a car leaves the the city traveling at 70 in chase of the first car.

A) how many hours will it take the second car to overtake the first car

B)How many miles will the cars be from the city when they meet?

Answer 1

The first thing you do is to come up with equations that define the distances traveled by each car.

car 1:
D1=50mph(t) where t is the time in hours and mph is miles per hour

car 2:
D2=70 mph(t)

the problem with this is that they have 2 different start times and these two t's aren't the same. To fix this you set all equations to the last car leaving. Since Car 1 has already traveled 50 miles by the time Car 2 leaves the adjusted equation becomes:

D1=50mph(t)+50miles and D2 stays the same at,
D2=70mph(t)
at t=0hr D1=50miles and D2=0miles
at t=1hr D1=100 miles and D2=70 miles
and so on,

The next step is to set these equations equal (where D1=D2) to each other and solve with respect to t;

D1=D2
50mph(t)+50miles=70mph(t) [subtracting 50m(t) from both sides]
50miles=70mph(t)-50mph(t)
50miles=(70mph-50mph)(t)
50miles=20mph(t)
(50miles/20miles)=t
(50/20)hrs=(5/2)hrs=(2 1/2)hrs = t in hours

with our original equations for D1 and D2 at 2 1/2 hours;
D1=50miles(2 1/2)+50 miles=175 miles
D2=70miles(2 1/2) = 175 miles

I hope this helps. I left out the laws used in each of the steps(i.e. associative, commutative etc.) it's been a while but they should be stated if you are in the proofs stage that you might not be in yet.

cheers
Mike

Answer 2

The first car is being chased by the second car?

And the second car didn't leave until an hour later?

The second car will NEVER take over the first car. Th first car sped up as soon as he hit the open road. He knows he's being followed, so he took backroads, and has made so many twists and turns, he's probably already gone back to his home city again, ditched the car for another one and is leisurely cruising his way to Mexico.

First rule of thumb when committing to a car chase: Don't wait an hour!

Answer 3

CAR A=50MPH
CAR B=70MPH

HOUR 1... CAR A HAS TRAVELED 50 MILES
HOUR 2... IT HAS TRAVELED 100 MILES
HOUR 3 ... IT HAS TRAVELED 150 MILES
HOUR 3.5... IT HAS TRAVELED 175

CAR B STARTS ONE HOUR BEHIND CAR A SO
HOUR 1...CAR B HAS TRAVELED 0 MILES
HOUR 2 ...CAR B HAS TRAVELED 70 MILES
HOUR 3...CAR B HAS TRAVELED 140 MILES
HOUR 3.5 ...CAR B HAS TRAVELED 175 MILES

SO WHEN THE TWO CARS MEET THEY WILL BE EXACTLY 175 MILES AWAY 3.5 HOURS LATER....AS FOR QUESTION A ASK HOW MANY HOURS IT WILL TAKE TO OVERTAKE CAR A...YOU WOULD HAVE TO KNOW THE LENGTH OF THE CARS TO DETERMINE THE EXACT PASSING POINT ...HOWEVER, SINCE IT ASKS HOW MANY HOURS IT WOULD TAKE I WOULD SAY 4 THOUGH IN REALITY YOU WOULD PASS >3.5 HOURS

Answer 4

The cars will meet at 3 hours 30min from starting time. The cars will be 175 miles from the city.

Answer 5

First car has 50 mile headstart....... First get the difference in speed 70 mph-50 mph =20 mph
with a difference of 20 mph how long will it take to make up the 50 mile headstart?

50 miles/20 mph =2.5 hrs

How far will they travel? You can use either vehicals speed times the hrs it takes
50 MPHx2.5 hrs= 125 miles

Answer 6

Hour 1: Car A - 50 mi., Car B - 0 mi

Hour 2: A - 100 mi, B - 70 mi

Hour 3: A - 150 mi, B - 140 mi

Hour 3.5: A - 175 mi, B - 175 mi

Answer 7

A) 10 hours

B) First car would be 50 miles; Second car will be 70 miles

Answer 8

car1: 50 100 150 200
car2: 0 70 140 * 210
hours: 1 2 3 4

A) 4 hours
B) about 190

Answer 9

10 hours later at 6.p.m. the first car is 3 hours at 50 miles for a total of 150 miles ahead!! the second is going 15 miles faster that the first one so it takes 10 hours at 15 miles=150 miles it takes to be even with the first one??

Answer 10

a 40 min because the guy traveling at 50 MILE PER HOUR HOUR. AND 1 HOUR passes so he has gone 50 miles. is the guy is going 70 miles per hour it will take him 40 min.

b i think 120 miles