Help with math homework!?

The cyclist ran a 27 km long road. At first he drove on the highway, then on the dirt road. The cycling speed on the highway was 18 km / h, on the dirt road - 15 km / h. It is known that he drove on the dirt road for 1h 15min longer than on the highway. Calculate how long the cyclist rode on the highway and how long on the dirt road!

4 Answers

Relevance
  • 1 month ago

     The cyclist ran a 27 km long road. 

     At first he drove on the highway, then on the dirt road. 

     The cycling speed on the highway was 18 km / h, on the dirt road - 15 km / h. 

     It is known that he drove on the dirt road 

     for 1 h 15 min longer than on the highway. 

     d + h = 27

     d/15 - h/18 = 1.5

     6d - 5h = 135

     5d + 5h = 135

     11d = 270

     d = 24.55

     The cyclist rode on the highway for a distance of 2.45 km

     and on the dirt road for 24.55 km.

    • Commenter avatarLogin to reply the answers
  • 1 month ago

    Suppose the cyclist drove on highway for T hours.

    So that distance covered on high way  =  18 * T  km  and  

    Distance covered on dirt Road = 15 (km/h) * ( T + 1 hr 15 min)  =  15 * (T + 1.25)

    But the total distance Cycled  = 27 km

    => 18 * T + 15 * (T + 1.25) =  27

    => T  =  0.25 hr

    Answers (for distances )

    =======================================  ======================

    Hence the distance covered on the high way  =  18 * ( 0.25 ) = 4.5 km

    And distance covered on dirt road = 22.5 km 

    =====================================================   ======

    For Time :

    ========================================

    On High way = 15 min.

    On Dirt Road = ( 0.25 + 1.25 )  =  1.50 hrs =  1 hrs 30 min.

    ===========================================

    • Commenter avatarLogin to reply the answers
  • 1 month ago

    The cyclist ran a 27 km long road

    d =  distance on dirt road

    27 - d = distance on highway

    ------------------------------

    he drove on the dirt road for 1h 15min longer than on the highway

    time = distance / speed

    time on dirt - time on highway = 1.25

        d/15        -      (27 - d)/18      = 1.25

    Multiply both sides by 90

    6d - 5(27 - d) = 112.5

    6d - 135 + 5d = 112.5

    11d = 247.5

    d = 22.5 miles on dirt

    27 - d = 4.5 miles on highway

    ----------------------------

    Time on dirt

    time = distance / speed

    t = 22.5/15

    t = 1.5 hours = 90 minutes <––––

    Time on highway

    he drove on the dirt road for 1h 15min longer than on the highway

    t = 1.5 - 1.25

    t = .25 hours = 15 minutes <–––––

    • Commenter avatarLogin to reply the answers
  • Anonymous
    1 month ago

    15 minutes and 90 minutes

    • Commenter avatarLogin to reply the answers
Still have questions? Get your answers by asking now.