SOLUTION: Mr Wong drove from his home to Mr Lee’s house in happy down at an average speed of 80 km/h. His speed for the last 1/4 of the journey was 7/8 of his average speed for the whole j

Question 1163873: Mr Wong drove from his home to Mr Lee’s house in happy down at an average speed of 80 km/h. His speed for the last 1/4 of the journey was 7/8 of his average speed for the whole journey. If he took 2 1/2 hours for the last 1/4 of the journey how long did it take to travel from his home to Mr Lee’s house?
Found 3 solutions by htmentor, Theo, MathTherapy:
Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
Let d = the total distance traveled
During the last 1/4 of the journey, the average speed was (7/8)*80 = 70 km/h
It took 2.5 h to travel d/4. Thus (d/4)/70 = 2.5 -> d = 700 km
The total time is given by the distance traveled divided by the avg. speed:
t = 700/80 = 8.75 hours

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
r * t = d
r = rate
t = time
d = distance
his average speed for the whole trip was 80 kilometers per hour.
let t = time and d = distance and the formula becomes:
80 * t = d
his average speed for the last 1/4 of the trip was 7/8 of his average sped for the whole trip.
7/8 * 80 = 70 kph.
the formula for the last 1/4 of the trip was therefore 70 * t = 1/4 * d
since the time for the last quarter of the trip was 2.5 hours, the formula for the last 1/4 of the trip becomes 70 * 2.5 = 1/4 * d
solve for d to get d = 4 * 70 * 2.5 = 700 kilometers.
the formula for the whole trip that was 80 * t = d becomes 80 * t = 700
solve for t to get t = 700 / 80 = 8.75 hours.
since 2.5 hours was expended for 1/4 of the trip, then 3/4 of the trip expended 6.25 hours.
the formula for 3/4 of the trip becomes r * 6.25 = 525
solve for r to get r = 525 / 6.25 = 84 kph.
this is all nice information to know, but the question was how long did it take to travel from his home to mr. lee's house.
the answer to that is 8.75 hours. *********
that's your solution.
it's not necessary to break it down any further than that.
however, assuming you did, then:
rate * time = distance for 3/4 of the distance becomes 84 * 6.25 = 525 + 70 * 2.5 = 175 for a total time of 8.75 hours to drive a total distance of 700 kilometers.
he traveled 84 kph for 525 km and 70 kph for 175 km for a total average of 80 kph for 700 km.
total time took 525/84 hours for 3/4 of the trip and 175/70 hours for 1/4 of the trip = total hours of 8.75 hours.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Mr Wong drove from his home to Mr Lee’s house in happy down at an average speed of 80 km/h. His speed for the last 1/4 of the journey was 7/8 of his average speed for the whole journey. If he took 2 1/2 hours for the last 1/4 of the journey how long did it take to travel from his home to Mr Lee’s house?

Time taken to travel the last ¼ of journey: 2½ hours
Speed during last ¼ of journey:
Therefore, ¼ of journey = 2½ * 70 = 175 km
If ¼ of journey is 175 km, then entire journey = 4(175) = 700 km
Let time taken to travel the entire journey, be T
Since , we get:
80T = 700 ----- Cross-multiplying
Time taken to travel the entire journey, or
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