Can someone help me solve this problem

Question

I don't even know how to start this problem r even solve it.:

Plane b is flying 30mph faster than plane a. Find the time it takes for plane b to travel 4150 miles if it takes plane a the same amount of time to travel 4000 miles

Answer 1

1. r_b = speed of Plane B and r_a = speed of Plane A

2. r_b = 30 + r_a or r_a = r_b - 30

3. Use the displacement formula (d = rt)

4. 4000 = r_a*t

5. 4150 = r_b*t

6. Substitute r_b - 30 for r_a

7. 4000 = (r_b - 30)t = r_b*t - 30*t

8. This is now a system of equations, so we can use elimination:

 

4000 = r_b*t - 30*t

4150 = r_b*t 

 

-1 (4000) = -1(r_b*t - 30*t)

4150       =  r_b*t

 

  -4000 = -r_b*t + 30*t

+ 4150 = r_b*t            

  150    =       + 30*t

 

150 = 30*t

150/30 = t

5 = t

 

t = 5 hours

 

Answer 2

This is a D-I-R-T (Distance-Is-Rate-times-Time) problem.  They usually have one of the variables that are the same or somehow related so that we can solve the problem.  In this problem "it takes plane a the same amount of time" as plane b, so we can set the times equal to "find the time."

 

Let r = rate that plane a is flying

 then plane b is flying at a rate of (r+30)

 

If d=rt, then t=d/r

 

           for plane a             for plane b

 t =     4000 / r      =       4150 / (r+30)

           4150r = 4000(r+30)             [cross multiply]

           4150r = 4000r + 120000       [distribute]

           150r = 120000                   [subtract 4000r from both sides]

              r = 800                      [divide both sides by 150]

    [important:  notice that we must first find r, then find the time]

 

         t= 4000 / 800       or   t= 4150 / (800+30)

           t = 5 hours

Answer 3

a. 5 hours