Mayra C.

asked • 12/10/15

what are there speeds

two cars are 300 miles apart and are traveling toward each other on the same road. they meet after driving 3 hours one car is traveling 20 mph slower than the other. what are there speeds

Atif Z.

Test
Report

12/10/15

1 Expert Answer

By:

Atif Z. answered • 12/10/15

Tutor
4.2 (5)

Tutor | Data Scientist | Data Engineer | Data Creative |

Atif Z.

Your car is a Mini Cooper
 
Emily Car is a Toyota Camry... 
 
Your are traveling 20 mile per hour faster than Emily's car.
 
And you both cross each other 3 hours later close to Samantha birthday party house!..
 
wooho!
 
Report

12/10/15

Atif Z.

Now lets do some calculations. :)
Report

12/10/15

Atif Z.

Your Car:  
 
speed = some_speed
Report

12/10/15

Atif Z.

Samantha Car - who is coming from opposite direction is
 
speed = some_speed - 20 mph
 
( she is travelling 20 mph slow than your mini cooper)
Report

12/10/15

Atif Z.

Now it takes 3 hours to cross each other so
 
time  = 3 hours.
 
Now lets find the distance.
 
The interesting thing is you will cover more distance in these 3 hours and Samantha will cover less, since she is driving slower.
Report

12/10/15

Atif Z.

Equation of distance is 
 
Distance = speed * time
 
we do not know the distance,
 
but we know our relative speeds to each to each other.
 
and! we know how long it took to cross each other (3 hours).
Report

12/10/15

Atif Z.

So we can say that we know it took 3 hours to cross each other and travel all together 300 miles, at what ever speed we were travelling.
 
 
Report

12/10/15

Atif Z.

So,
 
your car:
 
Distance = speed * time
 
distance = 300 miles
speed = some_speed mph
time = 3 hrs
 
 
Report

12/10/15

Atif Z.

Samantha's car:
 
distance = speed * time
 
distance = 300 miles
 
speed = some_speed - 20 mph
 
time = 3 hrs
Report

12/10/15

Atif Z.

Actually it was a combined effort of both of you guys to travel a distance of 300 miles, since both of you guys were all together 300 miles apart...
so here we go!!
Report

12/10/15

Atif Z.

Distance  = Speed * Time
 
your distance >>
 
Your_Distance + Samantha_Distance = Total_Distance
 
Your Distance = (some_speed mph * 3 hrs)
 
your distance = (3 * some_speed) miles
 
Samantha_distance = (some_speed - 20) mph * 3 hrs
Samantha_distance = (3 * some_speed) - (20 * 3 )
 
Samantha_distance = (3 * some_speed - 60 ) miles
Report

12/10/15

Atif Z.

As i mentioned earlier, it was a combined effort of both of you to travel 300 miles, since you guys were initially 300 miles apart.
 
and now we know each of you guys distances,
 
we can add them together to solve for speed!
 
 
Report

12/10/15

Atif Z.

Total_distance  = your_distance + Samantha_distance
 
300 = 3*some_speed + 3 * some_speed - 60
 
300 +60 = 6 * some_speed
 
360 = 6 * some_speed
 
some_speed = 360 / 6
 
some_speed = 60 miles per hour (mph)
Report

12/10/15

Atif Z.

aha! so what was your equation for distance........
 
see we used some_speed to tell the speed of your mini cooper!!
 
so you are travelling at 60 mph.....
 
Samantha's Toyota Camry was travelling 20 mph slower than yours!!!
 
so we can subtract 20 mph from your speed to get hers...
Report

12/10/15

Atif Z.

your speed = 60 mph
 
Samantha car speed =  60 - 20
 
Samantha car's speed = 40 mph
!!! we are done!!
Report

12/10/15

Mayra C.

i am super thankful thank you i have a final tomorrow and igot stuck on this question
 
Report

12/10/15

Atif Z.

no worries! best of luck on your finals.
Report

12/10/15

Atif Z.

FYI. , I used Samantha name instead of Emily to get the birthday party half way down the problem. 
Report

12/11/15

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.