Math Question?

b and d are hours spent bicycling and driving, respectively.
d = b-¼

12b = 36d
12b = 36(b-¼) = 36b-9
24b = 9
b = 9/24 = ⅜ hour

⅜ hour × 12 miles/hour = 4.5 miles

LET THE DISTANCE TO OFFICE BE X MILES

TIME = DISTANCE / SPEED

X /12 - X/36 = 1/4

MULTIPLY BOTH SIDES BY 36

3X - X = 9

2X= 9

X = 9/2 OR 4.5 MILES ANSWER

CHECK

4.5 /12 - 4.5 /36 = (13.5 -4.5) /36 =9/36 = 1/4

If Dr. Suzuki rides his bike to his​ office, he averages 12 miles per hour.
If he drives his​ car, he averages 36 miles per hour.
His time driving is 1/4 hour less than his time bicycling.
How far is his​ office?
Let t = time on the bike
Then (t - 0.25) = time in the car
It's easy to find t, then we can find the distance from that:
Write a distance equation; Distance = Speed * time
car distance = bike distance
36(t - 0.25) = 12t
36t - 9 = 12t
36t - 12t = +9
24t = 9
t = 9/24
t = 0.375 hrs
Find distance using time on the bike:
0.375 * 12 = 4.5 miles
Check solution using time in the car:
(.375 - 0.25) * 36
0.125 * 36 = 4.5 miles also

let d be the distance to his office.
d = 12t = 36(t-1/4) = 36t- 9
24t = 9
t = 3/8
d = 12(3/8) = 36/8 = 4.5 miles

12 t = 36 [ t - 1/4] ===> 24 t = 9 ====> t = 3 / 8 ===> distance is 12 ( 3/8) = 4.5 mile