Question 166790
A bicyclist rode up a mountain road at 12 km/h and then back down at 30 km/h. If the round trip toook 3.5 hours, how long did the ride up the mountain take?
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Remember: {{{Speed=Distance/time}}}, EQN 1
Given---{{{S[up]=12kph}}},{{{S[dn]=30kph}}};{{{time=3.5hrs}}}
*Note: {{{time=t[up]+t[dn]}}}, EQN 2
Via EQN 1, we get --> {{{Distance=Speed*time}}}
Since both distance is the same, we equate both going up and down:
{{{D[up]=D[dn]}}}
{{{S[up]*t[up]=S[dn]*t[dn]}}}, EQN 3
Via EQN 2, we get {{{t[dn]=time-t[up]}}}, EQN 4 ---> subst. in EQN 3:
{{{S[up]*t[up]=S[dn]*(time-t[up])}}}
{{{(12)*t[up]=(30)(3.5-t[up])}}}
{{{12*t[up]=105-30t[up]}}}
{{{12t[up]+30t[up]=105}}}
{{{42t[up]=105}}} ------> {{{cross(42)t[up]/cross(42)=cross(105)2.5/cross(42)}}}
{{{highlight(t[up]=2.5hrs)}}}, ANSWER in going up
For the record, Via EQN 2---> {{{t[dn]=3.5-2.5=1hr}}}, going down
* This just make sense, that it will take more time to go up than to go down.
Check Via EQN 3:
{{{12*2.5=30*1}}}
{{{30km=30km}}}
Thank you,
Jojo</pre>