x km/h. Write down an expression for the number of hours taken for the journey.
On his return journey from Malacca to Singapo, his average speed is reduced by 6km/h due to heavy traffic at the Causeway. Write down an expression for the time taken for the return journey.
If the return journey takes 20 minutes longer, form an equation in x and solve it to find the average speed for each journey, giving your answer correct to two decimal places.
2007-01-17 03:36:00 · 3 answers · asked by Zin Mar 1 in Science & Mathematics ➔ Mathematics
(I worked this through FOUR times before noticing that the difference in time on the way back was in MINUTES, while the rates were in km/HOUR....)
A motorist makes a journey of 240 km from Singapore to Malacca to visit his-in-laws at an average speed of x km/h. Write down an expression for the number of hours taken for the journey.
t = d / r = 240/x
On his return journey from Malacca to Singapo, his average speed is reduced by 6km/h due to heavy traffic at the Causeway. Write down an expression for the time taken for the return journey.
t = d / r = 240/(x - 6)
If the return journey takes 20 MINUTES (1/3 hour) longer, form an equation in x and solve it to find the average speed for each journey, giving your answer correct to two decimal places.
240/x + 1/3 = 240/(x - 6)
Multiply through by x(x - 6)
240(x - 6) + 1/3 x(x - 6) = 240x
240x - 1440 + 1/3 x² - 2x = 240x
1/3 x² - 2x - 1440 = 0
x² - 6x - 4320 = 0
This is unfactorable without using the quadratic.
x = (6 ± √(6² - 4(1)(-4320))/2 = (6 ± √17316)/2 = (6 ± 6√481)/2
x = 3 ± 3√481
But a negative rate makes no sense, so:
x = 3 + 3√481 ≈ 68.80 km/hr
So on the way back, he went an average of 62.80 km/hr.
Check:
on the way there, it took 240km/(68.80km/hr) = 3.489 hours, or 3 hours, 29.3 minutes.
on the way back, it took 240km/(62.80km/hr) = 3.822 hours, or 3 hours, 49.3 minutes...which is a difference of 20 minutes.
Whew, that took me a long time to get right.
2007-01-17 03:58:46 · answer #1 · answered by Jim Burnell 6 · 0⤊ 0⤋
You will never learn any thing by getting people online to do your work...
If you having trouble learning thos form of math ask you teacher for help...
Good luck in school
2007-01-17 03:43:55 · answer #2 · answered by Anonymous · 0⤊ 1⤋
t1 = 240/s1
t2 = 240/(s1-6)
s(avg) = 480/(2*t1+0.33)
2007-01-17 03:43:17 · answer #3 · answered by gebobs 6 · 0⤊ 0⤋