Mathematics, 17.07.2019 02:20 kelseydavid69

Dan took a train to his vacation spot. his train travels 75 miles each hour before making a stop. he left the station at 10: 00. phil is taking a vacation to the same spot, except his train travels 60 miles each hour before making a stop. phil’s train left the station at 8: 00. what time will they be in the same place?

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Answer from: Rochelle04

6pm

Step-by-step explanation:

Assumption: Both Dan and Phil both depart from the same station and arrive at the same station. (i.e they both travel the same distance)

Dan's travel speed is 75mph and Phil's travel speed is 60mph

Let Dan's travel time be $t_{Dan}$ and Phil's travel time be $t_{Phil}$

Use Formula Distance travelled = speed x time, hence

Dan's Distance Travelled =75 $t_{Dan}$

Phil's Distance Travelled =60 $t_{Phil}$

Because they travel the same distance, we can equate the 2

75 $t_{Dan}$ = 60 $t_{Phil}$

or $t_{Dan}$ = (60/75) $t_{Phil}$

$t_{Dan}$ = 0.8 $t_{Phil}$ -------> eq 1

We also know that Dan left at 10:00 and Phil left at 8:00. If they end up being at the same place, this means that Phil's journey will be 2 hours longer than Dan, or

$t_{Phil}$ = $t_{Dan}$ + 2------> eq2

we can solve the system of 2 equations to get

$t_{Phil}$ = 10 hrs

$t_{Dan}$ = 8 hrs

If Phil left at 8:00 am, he will be in the same place as Dan at 8:00 + 10 hrs = 6 pm.

Double Check:

If Dan left at 10:00, he will be in the same place as Phill at 10:00 + 8 hrs = 6 pm.

Answer from: Quest

Answer: 10pi

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

Find the length of ac express your answer in terms of pi

Answer from: Quest

think about it deeply and passionately about this property

i am sorry

Find the size of angle xyz give your answer to one decimal place. rectangle triangle (angle 90°) and

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