Final answer:
Jack and Tom will pass each other 4 hours after they start driving at 10.30 a.m. They will be about 40 km apart at 2.45 p.m.
Step-by-step explanation:
To determine when Jack and Tom will pass each other, we need to calculate the time it takes for each of them to travel a distance that adds up to the total distance between Town X and Town Y.
Jack is driving at 70 km/h and Tom is driving at 90 km/h. Since their speeds are in opposite directions, we can add them to find their combined speed, which is 70 km/h + 90 km/h = 160 km/h.
To find the time it takes for them to cover the distance of 640 km, we divide the distance by the combined speed: 640 km ÷ 160 km/h = 4 hours.
(a) Since they both started at 10.30 a.m., they will pass each other 4 hours later, at 2.30 p.m.
(b) To determine how far apart they are at 2.45 p.m., we need to calculate the distance each of them has traveled in that time. Jack will have traveled for 4 hours and 15 minutes (2.45 p.m. - 10.30 a.m.), which is about 4.25 hours. His distance traveled is 70 km/h × 4.25 hours = 297.5 km. Tom will have traveled for the same amount of time, so his distance traveled is 90 km/h × 4.25 hours = 382.5 km. Therefore, they will be approximately 640 km - (297.5 km + 382.5 km) = 640 km - 680 km = -40 km apart, which means they have passed each other and are now on opposite sides of their starting points.