let [tex] V_{b}[/tex] be velocity of bicycle
let [tex] t_{b}[/tex] be time traveled of bicycle
Given:
[tex] V_{m} = V_{b}+15 kph [/tex]
[tex] t_{m} = t_{b} -2 hrs[/tex]
[tex] d_{b} = d_{m} = 60 km[/tex]
formula:
[tex]d=Velocity[/tex] [tex]x[/tex] [tex]time[/tex]
[tex]time= \frac{distance}{Velocity} [/tex]
Solution:
time for bicycle
[tex] t_{b}= \frac{60}{ V_{b} } [/tex]
use [tex] t_{b} [/tex] on [tex] d_{m} = V_{m} [/tex] [tex]x[/tex] [tex] t_{m} [/tex]
[tex]60km=( V_{b}+15)( \frac{60}{ V_{b} }-2) [/tex]
[tex] V_{b} =15kph[/tex]
use [tex] V_{b} =15kph[/tex] on [tex] t_{b}= \frac{60}{ V_{b} } [/tex]
[tex] t_{b}= \frac{60}{15kph} [/tex]
[tex] t_{b} = 4 hrs[/tex]
solve for [tex] t_{m} [/tex]:
[tex] t_{m} = 4hrs -2 hrs[/tex]
[tex] t_{m} =2hrs[/tex]
solve for [tex] V_{m} [/tex]:
[tex] V_{m} = 15kph+15 kph [/tex]
[tex] V_{m} =30kph[/tex]
