Let Jessica's distance travelled in 1 hour be 1u km

She started 2h 30 min earlier than Joey.

2h 30 min = 2½ h = 2.5h


By the time Joey started her journey, Jessica would have already travelled 2.5u km


Since Joey's speed is faster by 30km/h,
Her distance travelled in 1 hour = 1u km + 30 km

So for 90 min,
90 min = 1h 30 min = 1½ h = 1.5 h

Her distance travelled in 90 min = 1.5 × 1u km + 1.5 × 30 km

= 1.5u km + 45 km


In the same 90 min, Jessica's only travelled 1.5u km.


Total time Jessica spent driving = 2.5h + 1.5h
= 4h

Total distance she drove = 4u km

thank you

Distance they are apart = total distance travelled by the two people

Total distance travelled by the two of them

= Jessica's distance + Joey's distance
= 4u km + 1.5u km + 45 km
= 5.5u km + 45 km


So,

5.5u km + 45 km = 320 km

5.5u km = 320 km - 45 km

5.5u km = 275 km

1u = 275 ÷ 5.5

1u = 50

So,

Jessica travels 50km in 1 hour.

Her speed is therefore 50km/h

Please check the updated comments.

I understand how to solve these types of questions now thank you

Check:

Distance travelled by Jessica in 2h 30 min

= 50km/h × 2.5h
= 125km

Distance travelled by Jessica in the next 90 min

= 50km/h × 1.5h
= 75km

Total distance Jessica travelled
= 125km + 75km
= 200km

She is now 200km away from the starting place.

Joey's speed = 50km/h + 30km/h
= 80km/h

Distance travelled by Joey in 90 min
= 80km/h × 1.5h
= 120km

She is now 120km away from the starting place.


Distance the two of them travelled altogether
= 200km + 120km
= 320km

They are now 320km apart. ✓