Bob takes the subway to work and uses an escalator at the railway station. If Bob runs up 8 steps of the escalator, then it takes him 46.5 seconds to reach the

Question

Bob takes the subway to work and uses an escalator at the railway station. If Bob runs up 8 steps of the escalator, then it takes him 46.5 seconds to reach the top of the escalator. If he runs up 13 steps of the escalator, then it takes him only 39.0 seconds to reach the top. How many seconds would it take Bob to reach the top if he did not run up any steps of the escalator?

Answer 1

Let N be the number of steps to get to the top of the escalator

and v the speed of the escalator in steps/second, The speed of

the escalator is  constant.

 

Bob runs 8 steps and he reaches the top in 46.5 seconds

The escalator must traverse (N - 8) steps in this same time.

v = (N - 8)/46.5

 

Bob runs 13 steps and he reaches the top in 39 seconds
The escalator must traverse (N - 13) steps in this same time.
v = (N - 13)/39

 

∴ v = (N - 8)/46.5 = (N - 13)/39

Solving this results in N = 39 steps and the escalator moving at

2/3 steps/second. When Bob is not moving it would take(39 steps)  * (3/2 seconds/step) = 58.5 seconds to reach the top.

Answer 2

(39 - 46.5) / (13 - 8) = -1.5         calculate "slope"

 

y = -1.5x + b                             slope-intercept form

46.5 = -1.5(8) + b                      substitute one pair

46.5 = -12 + b                           distribute

56.5 = b                                    add 12 to both sides

 

y = -1.5x + 56.5

 

Standing still he would reach the top in 56.5 second.