Algebra help!!?

Question

Two cars travel the same distance. The first car travels at a rate of 40 miles per hour and reaches its destination in t hours. The second car travels at a rate of 55 miles per hour and reaches its destination 3 hours earlier than the first car. How long does it take for the first car to reach its destination?

Answer 1

Distance =Rate X Time
Distance traveled is the same for both cars
First car: 40(t)
Second car: 55(t-3)
40t =55(t-3)
40t =55t-165
15t=165
t=11
It takes the first car 11 hrs. to reach its destination.

Answer 2

Okay, this relies on the basic formula that distance=speed*time.

We are given that the first car travels at 40mph and gets there in t hours.

So the distance = 40t

The second car travels at 55mph, and we need to find its time.

distance = 55 * time

substituting distance = 40t:

40t = 55 *time
time = (40t)/55


Okay we are given that this time is 3 hours less than t. so this means that (40t)/55 = t-3

so all we need to do is solve this equation to find t

multiple both sides by 55
40t = 55 (t-3)

expand out brackets
40t = 55t - 165

add 165 to both sides, and subtract 40t
165 = 15t

divide both sides by 15
11 = t





so this means the first car took 11 hours to reach its destination.

hope this helps!

Answer 3

Speed of first S1= D/T1
Speed of second S2=D/T2
Since, D is same for both.
Therefore, S1 x T1=S2 x T2
40 x T1 = 55 x (T1-3), Since Second car reaches 3 hours earlier
Solving the above,
15T1 =165
therefore, T1=11
So, the first car takes 11 hours, second car takes 8 hours, (T1-3)

Answer 4

the time taken by the first car = x hrs

the time taken by second car = (x-3) hr

the distance traveeled by first car = speed*time =40x mi

the distance travelled by second car = 55(x-3) mi

55(x-3) = 40x

55x - 165 = 40x

15x = 165

x = 165/15 = 11 hrs

Answer 5

distance = time * speed
d=40t
d = 55(t-3)
We kinda hope that d = d so
55(t-3) = 40t
Solve for t and you're done.

Doug

Answer 6

40t=55(t-3)
40t-55t=-165
-15t=-165
t=11hours