Ferb will reach Perry the Platypus first, taking approximately 3.32 hours, while Phineas will take about 3.38 hours based on their respective map scales and speeds.
To determine who will reach Perry the Platypus first, we need to calculate the time it takes for each of them to travel from NYC to Boston using their respective maps and speeds.
Let's start with Phineas:
Phineas' map scale: 1.5 cm to 32 miles
Distance from NYC to Boston on Phineas' map: 10.8 cm
The real distance (D) Phineas needs to travel is calculated using the scale:
Distance = 10.8 cm * (32 miles / 1.5 cm) = 10.8 cm * 21.333... = approximately 229.714... miles
Now, we can use the formula Time = Distance / Speed to find the time it takes for Phineas to travel the distance:
Time = 229.714... miles / 68 mph = approximately 3.38 hours
Now, let's do the same for Ferb:
Ferb's map scale: 2.5 cm to 23 miles
Distance from NYC to Boston on Ferb's map: 23.5 cm
The real distance (D) Ferb needs to travel is calculated using the scale:
Distance = 23.5 cm * (23 miles / 2.5 cm) = 23.5 cm * 9.2 = approximately 216.2 miles
Now, we can use the formula Time = Distance / Speed to find the time it takes for Ferb to travel the distance:
Time = 216.2 miles / 65 mph = approximately 3.32 hours
Comparing the times, we can see that Ferb will reach Perry the Platypus first, as he will take approximately 3.32 hours, while Phineas will take approximately 3.38 hours.
Complete question:
Phineas and Ferb are going to visit Perry the Platypus in Boston, MA They are going to drive different routes from NYC to see who can get there faster. Each has their own map and their own vehicle Phineas' map has a scale of 1.5 cm : 32 miles and NYC is 10.8 cm away from Boston. Ferb's map has a scale of 2.5 cm : 23 miles and NYC is 23.5 cm away from Boston. If Phineas drives at a constant rate of 68 miles per hour and Ferb drives at a constant rate of 65 miles per hour. who will reach Perry the Platypus first? Show your work and explain how you know.