SOLUTION: Ethan goes on a charity journey. He walks one-tenth of the way at 6km/h, runs one-sixth at 12 km/h, cycles one-fifth at 24km/h, completes the remaining 32km by car at 48km/h. How m

Question 205480This question is from textbook Longman Mathematics for IGCSE Book 1
: Ethan goes on a charity journey. He walks one-tenth of the way at 6km/h, runs one-sixth at 12 km/h, cycles one-fifth at 24km/h, completes the remaining 32km by car at 48km/h. How many kilometres does he travel and how long does it take? This question is from textbook Longman Mathematics for IGCSE Book 1

Found 2 solutions by Edwin McCravy, J2R2R:
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
Ethan goes on a charity journey. He walks one-tenth of the way at 6km/h, runs one-sixth at 12 km/h, cycles one-fifth at 24km/h, completes thje remaining 32km by car at 48km/h. How many kilometers does he travel and how long it take?

Let the total distance = D km. Distance walking = Distance running = Distance cycling = Distance by car = Total distance = The LCD is 30. So we multiply every term by 30: Subtract 960 from both sides: Subtract 30D from both sides: Divide both sides by -16 So his total distance is 60 km. Distance walking = Distance running = Distance cycling = Distance by car = Now we use Time walking = Time running = Time cycling = Time by car = Total time = Total time = Edwin

Answer by J2R2R(94) (Show Source): You can put this solution on YOUR website!
D is the total distance and the time (t) is in hours so,

First section: D/(10*6) = t1

Second section: D/(6*12) = t2

Third section: D/(5*24) = t3

Last section: 32/48 = t4

He has travelled D/10 + D/6 + D/5 (=7D/15) of the way so has 8D/15 left which is 32 km. Therefore D = 60 km.
t1 = 60/60 = 1 hour
t2 = 60/72 = 50 minutes
t3 = 60/120 = 30 minutes
t4 = 32/48 = 40 minutes
Total time T = t1 + t2 + t3 + t4 = 3 hours.

Checking:
6 km at 6 km/h is an hour (6 km is 1/10)
10 km at 12 km/h is 50 minutes (10 km is 1/6)
12 km at 24 km/h is 30 minutes (12 km is 1/5)
32 km at 48 km/h is 40 minutes (32 km is 8/15)

Total distance is 60 km and total time is 3 hours.
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