Answer:
The speed at which Carol needs to drive to meet Irvin at Bananatown at exactly the same time is approximately 47.188 miles per hour
Step-by-step explanation:
The given information are;
The location of Bananatown from Appletown = 143 miles east and 45 miles north
The location of Coconutville from Appletown = 98 miles east and 32 miles south
Taking Appletown as the origin, we have;
The slope, gradient of highway 42 = 45/143
The equation of a line representing highway 42 is given as follows;
y - 0 = 45/143 × (x - 0)
y = 45/143·x
Therefore, at Coconutville, where x = 98, we have, y = 45/143 × 98 ≈ 30.84 miles north
Total distance north Carol has to drive to get to highway 42 = 32 + 30.84 = 62.84 miles
Total distance along highway 42 Carol will drive to get to Bananatown = √((143 - 98)² + (45 - 30.84)²) ≈ 47.175 miles
Total distance Carol drives to Bananatown = 47.175 miles + 62.84 miles ≈ 110.015 miles
The total distance Irvin needs to drive to arrive at Bananatown = √(143² + 45²) ≈ 149.91
The total distance Irvin needs to drive to arrive at Bananatown ≈ 149.91 miles
The time it takes Irvin to arrive at Bananatown = (149.91 miles)/(45 mph) ≈ 3.33 hours
The time he arrives at Bananatown = 8 a.m. + 3.33 hours ≈ 11.33 a.m.
The time available for Carol to meet Irvin at Bananatown at exactly the same time = 11.33 a.m. - 9 a.m. = 2.33 hours
Therefore, the speed at which Carol needs to drive = (110.015 miles)/2.33 hour ≈ 47.188 miles per hour
The speed at which Carol needs to drive to meet Irvin at Bananatown at exactly the same time ≈ 47.188 miles per hour.
