A jet flew from tokyo to bangkok, a distance of 4800km. On the return trip, the speed was decreased by 200 km/h. If the difference in the times of the flight was 2 hours, what was the jets speed from bangkok to tokyo?
A jet flew from tokyo to bangkok, a distance of 4800km. On the return trip, the speed was decreased by 200 km/h. If the difference in the times of the flight was 2 hours, what was the jets speed from bangkok to tokyo?
Hello, Chr2010!
A jet flew from Tokyo to Bangkok, a distance of 4800km.
On the return trip, the speed was decreased by 200 km/hr.
If the difference in the times of the flight was 2 hours,
what was the jet's speed from Bangkok to Tokyo?
The jet flew 4800 km from Bangkok to Tokyo at km/hr.
. . This took hours.
The jet flew 4800 km from Tokyo to Bangkok at km/hr.
. . This took hours.
The difference in time was 2 hours: .
Multiply by
This equation simplifies to: .
. . whoch factors: .
. . and has roots: .
The jet's speed from Bangkok to Tokyo was 600 km/hr.
Soroban started by choosing a letter to represent the quantity he wanted to find- in this case he let "x" represent the speed flying from Bangcock to Tokyo. You are told that the distance is 4800 km and should know that "speed= distance/time" so if we let be the time the flight took, so, solving that for , .
We don't know so we can use that equation alone to find x. But we also know that "On the return trip, the speed was decreased by 200 km/h". Since is the speed on the return trip, the speed on the first leg must be 200 more: x+ 200. The time to fly the same 4800 is . That flight was at a faster speed so of course, it takes less time- 2 hours less: , the difference in times, is 2 hours:
Get rid of the fractions by multiplying both sides of that equation by x(x+ 200) and you get the quadratic equation Soroban gave.