Francisco went on a bike ride of 120 miles.

Question

He realized that if he had gone 24 mph faster, he would have arrived 16 hours sooner. How fast d? 

 

 

Answer 1

Let Francisco actual speed is =  x mph

When incresing his speed 24mph then speed = x  + 24 mph

Speed = distance / time

Time = distance / speed

t = 16 hours ,d = 120miles

Fransico reached  120miles with actual speed timeT₁= 120/x

Fransico reached  120miles with his increasing speed  timeT₂= 120/(x + 24)

Difference between two times is 16 hours.

 120/x  - 120/(x + 24) = 16

[120(x + 24) - 120x ]/x (x + 24) = 16

120(x + 24) - 120x  = 16x (x + 24)x ²

120x + 2880 - 120x = 16x ² + 384x

2880 = 16x ² + 384x

16x ² + 384x  - 2880 = 0

x ² + 24x  - 180 = 0

x ² + 30x - 6x  - 180 = 0

x ( x  + 30 ) - 6(x + 30) = 0

( x  + 30) (x  - 6) = 0

x  = -30 and x  = 6

Choose positive value for x .

So x  = 6

Fransico actual speed is 6 mph.

check

x = 6, x +24 = 30

T₁ = 120/6 = 20 hours

T₂ = 120/30 = 4 hours.

T₁ - T₂ = 20 - 4 = 16 hours.

Comments

It helped a lot, Thank You :)