Verified answer

[tex] \huge{\pmb{\mathtt{\boxed{\pink{A} \red{n}\orange{s}\purple{w}\green{e}\blue{r}}}}}[/tex]

- Let p be the speed of the plane in still air and w be the speed of the wind.

- The speed of the plane with the wind is p + w and the speed of the plane against the wind is p - w.

- The distance traveled by the plane in both cases is 1120 km.

- The time taken by the plane with the wind is 1 hour and 20 minutes, which is 4/3 hours.

- The time taken by the plane against the wind is 1 hour and 24 minutes, which is 7/5 hours.

- Using the formula distance = rate x time, we can set up two equations:

p + w = 1120 / (4/3)

p - w = 1120 / (7/5)

- To solve for p and w, we can add the two equations to eliminate w:

2p = 1120 / (4/3) + 1120 / (7/5)

2p = 840 + 800

2p = 1640

p = 820

- To find w, we can substitute p = 820 in either equation:

820 + w = 1120 / (4/3)

w = 1120 / (4/3) - 820

w = 280

- Therefore, the speed of the plane in still air is 820 km/h and the speed of the wind is 280 km/h.

[tex]\color{Red}\huge{\mathcal{\bold{\boxed{(⁠•⁠‿⁠•⁠)}}}}[/tex]