Aman starts out on a trip driving his car at a constant rate of 48 mph. a man riding a motorcycle starts out on the same route 1 1 2 12 hours later, traveling at a constant rate of 64 mph. how long will the car have been traveling when the motorcycle catches up?

The distance cover by car when motorcycle catches up is 2304 miles .

Step-by-step explanation:

Given as :

The speed of the car = S = 48 mph

Let The distance cover by car = D miles

The time taken by car to cover D distance = T hours

Again

The speed of motorcycle = s = 64 mph

Let The distance cover by motorcycle = d miles

The time taken by motorcycle to cover d distance = (T + 12) hours

According to question

The motorcycle catches the car , So distance cover by both is equal

So, distance cover by car = distance cover by motorcycle

∵ Distance = speed × time

Or, D miles = d miles

Or, Speed × Time = speed × Time

Or, 48 mph × T hour = 64 mph × (T - 12) hour

Or, 48 T = 64 T - 64 × 12

Or, 64 T - 48 T = 768

Or, 16 T = 768

∴  T =

i.e T = 48 hours

So, Time taken by car to cover d distance = 48 hours

∵ Distance = speed × time

So, Distance = 48 mph × 48 hours

∴  Distance = 2304 miles

So, The distance cover by car = D = 2304 miles

Hence, The distance cover by car when motorcycle catches up is 2304 miles . Answer

  6 hours

Step-by-step explanation:

The car has a head start of (48 mi/h)(1.5 h) = 72 mi. The motorcycle is catching up at the rate of (64 -48) = 16 mi/h. At that rate, the motorcycle will catch up to the car in (72 mi)/(16 mi/h) = 4.5 h.

When the motorcycle catches the car, it will have been traveling 4.5 hours. The car traveled 1.5 hours longer. The car will have been traveling for 6 hours.

Check

They will meet at a distance of 48·6 = 288 = 64·4.5 miles from the start.

Alternate Solution

If you like, you can write an equation for the distance covered from the time the car starts:

  car's distance = 48t

  motorcycle's distance = 64(t -1.5)

These distances are equal when ...

  48t = 64t - 96

  96 = 16t . . . . . . . add 96-48t

  96/16 = 6 = t . . . . the motorcycle catches up 6 hours after the car starts.

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Note that in this solution, we are solving for the time from the car starting. In the above "word" solution, we solved for the time from the motorcycle starting, then added the time before the motorcycle started.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.