SOLUTION: Alan cycles everyday from home to school and back. The school is 6km from his home. He cycles at an average speed of x km/h in his outward journey from home to school. On his retur

Algebra ->  Equations -> SOLUTION: Alan cycles everyday from home to school and back. The school is 6km from his home. He cycles at an average speed of x km/h in his outward journey from home to school. On his retur      Log On


   

Question 957405: Alan cycles everyday from home to school and back. The school is 6km from his home. He cycles at an average speed of x km/h in his outward journey from home to school. On his return journey from school to home he cycles 3 km/h faster.
1.Find in terms of x the time in hours taken for the outward journey.
2.Find in terms of x the time in hours taken for the return journey.
3.If the return journey takes 20 minutes less than then outward journey,use the result an obtained in part i and ii to show that x^2+3x-54=0.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1)
+d+=+6+ km
+x+ = rate in km/hr
+d+=+x%2At+
+6+=+x%2At+
+t+=+6%2Fx+
--------------
(2)
Return journey:
+d+=+6+ km
+x+%2B+3+ = rate in km/hr
+6+=+%28+x+%2B+3+%29%2At+
+t+=+6%2F%28+x+%2B+3+%29+
-------------------
You are given:
+6%2F%28+x%2B3+%29+=+6%2Fx+-+20%2F60+
( note that I converted +20+ min to hours )
+6%2F%28+x%2B3+%29+=+6%2Fx+-+1%2F3+
Multiply both sides by +x%2A%28+x%2B3+%29%2A3+
+6%2A%283x%29++=+6%2A%283%2A%28x%2B3%29%29+-+x%2A%28+x%2B3+%29+
+18x+=+6%2A%28+3x+%2B+9+%29+-+x%5E2+-+3x+
+18x+=+18x+%2B+54+-+x%5E2+-+3x+
Subtract +18x+ from both sides
+0+=+-x%5E2+-+3x+%2B+54+
Multiply both sides by +-1+
+x%5E2+%2B+3x+-+54+=+0+