The rate of the plane in still air is 710 km/hr and the rate of the wind is 160 km/hr
Step-by-step explanation:
Let Va = the velocity of the airplane
Let Vw = the velocity of the wind
When flying with the wind:
(Va+Vw)*(5 hours) = 4350
5Va + 5Vw = 4350
5Vw = 4350 - 5Va
Vw = 870 - Va
When flying against the wind:
(Va-Vw)*(7 hours) = 4200 km
7Va - 7Vw = 4200
Substitute 870-Va for Vw and solve for Va:
7Va - 7(870-Va) = 3850
7Va -6090 + 7Va = 3850
14Va = 9940
Va = 710 km/hr
Rate of wind:
Vw = 870 - Va
= 870 - 710
= 160 km/hour
Therefore, the rate of the plane in still air is 710 km/hr and the rate of the wind is 160 km/hr