Mayra C.
asked • 12/10/15what 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
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1 Expert Answer
Atif Z. answered • 12/10/15
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Tutor | Data Scientist | Data Engineer | Data Creative |
hi Mayra, here we go !
So we have two cars. Now image you are going to a birthday party at Samantha's place.
You live in Oakville, ON and Samantha lives in Toronto downtown.
Now you call you buddy Emily and she is coming to Samanthas party as well, and she lives in Markam, ON.
So here we are.
This is your house ( |^|) ......................driving to Samanthas party in TO...>>>>>>>>>>>>>>>> car is travelling at a speed that you do not car..( most likely within speed limits)...>>>>>> and it took you 3 hours to reach Samanthas place...................................................................................................................................................................
...You travel >>>> way ...........................[ Samantha's Birthday party house]..........<<<<...Emily is come from opposite direction to the party....
<<<<<<<<.......................<<<<<<<<..............now here your Friend Emily who is comming from the opposite side of the town from Markam....is also in the car ......driving at a speed 20 mile per hour slow than you.......going to Samanthas party in TO down town...
Now lets see :)
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!
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12/10/15
Atif Z.
Now lets do some calculations. :)
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12/10/15
Atif Z.
Your Car:
speed = some_speed
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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)
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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.
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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).
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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.
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12/10/15
Atif Z.
So,
your car:
Distance = speed * time
distance = 300 miles
speed = some_speed mph
time = 3 hrs
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12/10/15
Atif Z.
Samantha's car:
distance = speed * time
distance = 300 miles
speed = some_speed - 20 mph
time = 3 hrs
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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!!
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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
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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!
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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)
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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...
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12/10/15
Atif Z.
your speed = 60 mph
Samantha car speed = 60 - 20
Samantha car's speed = 40 mph
!!! we are done!!
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12/10/15
Mayra C.
i am super thankful thank you i have a final tomorrow and igot stuck on this question
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12/10/15
Atif Z.
no worries! best of luck on your finals.
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12/10/15
Atif Z.
FYI. , I used Samantha name instead of Emily to get the birthday party half way down the problem.
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12/11/15
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Atif Z.
12/10/15