Lily is meeting Jon at a certain time. If she drives at 80km/h,she will be 20min late.If she drives at 60km/h,she will be 45min late.?

suppose she's not late and it takes her t hours to meet Jon.
Let d be the distance between her and joh. Since she's 20 minutes late, she would have to travel for another 20 minutes to cover the distance.
d = 80(t+20/60)



and
d = 60(t+45/60)

set those two equations equal to each each other.
80(t+20/60) = 60(t+45/60)
t = 11/12 hour

d = 80(11/12 + 20/60) = 100 km

so it would take her 100/90 = 10/9 hr to complete.

Let d km be the distance of the journey.

(Time taken for driving at 80 min/h) + (20/60 h) = (Time taken for driving at 60 km/h) - (45/60 h)
(d/80) + (20/60) = (d/60) - (45/60)
[(d/80) + (20/60)] × 240 = [(d/60) - (45/60)] × 240
3d + 80 = 4d - 180
d = 100
Distance = 100 km

Time taken to complete the journey if she drives at 90 km/h
= (100 km) / (90 km/h)
= 1 and (1/9) h

hint:
find d/90 , hours
with
d/60 - d/80 = 5/12

Let t be the time it takes her to get there, in hours

Distance = Speed * Time

d = 80 * (t + 20/60)
d = 60 * (t + 45/60)

80 * (t + 1/3) = 60 * (t + 3/4)
4 * (t + 1/3) = 3 * (t + 3/4)
4t + 4/3 = 3t + 9/4
4t - 3t = 9/4 - 4/3
t = 27/12 - 16/12
t = 11/12

She is supposed to be there in 55 minutes

80 * (11/12 + 20/60) =>
80 * (11/12 + 4/12) =>
80 * (15/12) =>
80 * (5/4) =>
20 * 5 =>
100

She has to travel 100 km

100 / 90 =>
10/9

It'll take her 10/9 hours

(10/9) * 60 =>
600/9 =>
200/3 =>
66.666666....

1 hour 6 minutes 40 seconds