Math--HELP?

Question

I need help, I don't remember how to do this?
You can give me the answer if you want, but I still have to show my work, so please help me show my work.

A car leaves the store at a constant rate of 50 miles per hour to New York.
A second car leaves for New York 1 and 3/4 hours later. The second car travels at a constant rate of 75 miles per hour.
How many hours after the second train leaves the shop will it pass the first car?

Answer 1

You never said anything about a train! :-)

Distance = Rate * Time

Since both distances will be the same, you set the two rate * time equations equal and solve:

50 * (t + 1.75) = 75 * t
50t + 87.5 = 75t
25t = 87.5
t = 3.5

The second car will pass the first car after 3½ hours. :-)

Hey, Vic. Didn't you know that everywhere is more than 3½ hours from New York? XD

Answer 2

the easy way is form a chart.
hours car 1 car 2
1 50 0
2 100 12.5
3 150 87.5
4 200 162.5
5 250 237.5
6 300 313.5
so just under 6 hours for a more math intensive anwser
75T=D
50(T+1.75)=D
75T=50(T+1.75)
75T=50T+87.5
25T=87.5
T=3.5
but because car 1 had a head start you add 1.75 hours to 3.5 hours and end up with 5 hours and 15 min. so this is the moment they pass each other.

Answer 3

Good answer by dave, BUT if the cars are in a city that takes them less than 3 hours to get to NY, the second car will never pass the first one

Answer 4

Depends on the distance from the store to the city. Maybe the first one gets there early, checks in to a hotel, heads down to the bar, orders a Tequila Sunrise, buys a newspaper and sits down and reads it for a little while, waiting for the other guy to show up.

Answer 5

t0 = 0 [the first car's departure time]
t1 = 1.75 [2nd car's depateru time]

v1 = 50 [mph]
v2 = 75 [mph]


many ways to approach the solution:

in 1.75 hours, car#1 has gone 50*1.75 = 87.5 miles

d1 = 87.5 + t*50
d2 = 0 + t*75
d1 = d2 [ the "distance travelled" when #2 catches #1] =>

87.5 + 50t = 75t
87.5 = 25t
t = 87.5/25 = 3.5

means that 3.5 hours after the 2nd car starts, it wil 'catch" the first car.

[statemens of "trains" and "shops" and "stores" and "NewYork" don't necessarily make much sense, so I essentially dimissed them .. maybe this is not a correct reading ... I don't know.

the math is fairly solid tho

good luck

Answer 6

I assume you mean second car not second train

x = number of hours second car passes first car

first car goes 50*(x+1.75)

second car goes 75 (x)

50(x+1.75)=75x

50x + 87.5=75x
87.5=25x
3.5=x

car 1 travels 50*(3.5+1.75)=262.5 miles

car 2 travels 75*3.5=262.5 miles

Answer 7

train?