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                            Slow     :    Fast              : Diff    

Speed                60          :     80                :             

Ratio of time     4           :      3                  :    1       

Actual time      28min    : 21 min           :   7min (diff in time) –  updated

Same distance =  (28/60) x60 =or  (21/60) x80 = 28km#

Time = Distance/speed

= 28/100 h = 0.28 x 3600 sec = 1008 seconds#


Or by algebra:

Distance when fast = Distance when slow

80 . t                         = 60 . (t + 7/60)

20t = 7

t= 7/20 h = 21 mins when travelling at 80km/h.

Distance office to home = 80 x 7/20 = 28km#

Other workings as above.

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how do you get this?

Actual time      28min    : 21 min           :   7min 

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Hi. multiply by 7 (given difference in time is 7 mins).

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(a)
8.23 am to 8.30 am ——- 7 min = (7/60) h
Assume time taken is t if he drive at an average speed of 60 km/h,
60t ——- 80 x [t – (7/60)] = 80t – 9 1/3
t ——- 9 1/3/(80 – 60) = 28/60
60 x (28/60) = 28 or 80 x (28/60 – 7/60) = 28

(b)
28/60 h = 28 min
28 min before 8.30 am ——- 8.02 am (starting time)
or
28/80 = 0.35
0.35 h = 21 min
21 min before 8.23 am ——- 8.02 am (starting time)

28/100 = 0.28
0.28 h = 1008 s

Ans : (a) 28 km; (b) 1008 s.

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