Question

Fwam and Eva are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Fwam is 327 miles away from the stadium and Eva is 396 miles away from the stadium. Fwam is driving along the highway at a speed of 42 miles per hour and Eva is driving at speed of 65 miles per hour. Let FF represent Fwam's distance, in miles, away from the stadium tt hours after noon. Let EE represent Eva's distance, in miles, away from the stadium tt hours after noon. Write an equation for each situation, in terms of t, commat, and determine how far both Fwam and Eva are from the stadium at the moment they are an equal distance from the stadium.

Answer 1

Fwam and Eva will be at equal distances from the stadium 3 hours after noon, both being 201 miles away from the stadium at that time.

Step-by-step explanation:

To determine the distance from the stadium that Fwam (FF) and Eva (EE) will be at any time t hours after noon, we can use the formula for constant speed motion: distance = initial distance - speed × time.

For Fwam, this is FF = 327 miles - 42 miles/hour × t, which simplifies to FF = 327 - 42t.

For Eva,

we have EE = 396 miles - 65 miles/hour × t,

which simplifies to EE = 396 - 65t.

To find when they are the same distance from the stadium, we set the two equations equal to each other and solve for t:

327 - 42t = 396 - 65t

Adding 65t to both sides and subtracting 327 from both sides gives:

23t = 69

Dividing by 23, we find t = 3.

This means that 3 hours after noon, both Fwam and Eva are the same distance from the stadium.

To find this distance, we can substitute t = 3 back into either equation:

FF = 327 - 42 × 3

= 327 - 126

= 201 miles

Therefore, after 3 hours, both Fwam and Eva are 201 miles from the stadium.